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Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium

May 28, 2018May 28, 2018 by Prasanna

Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium

Chapter 11 Rotational Dynamics and Static Equilibrium Q.1CQ
Two forces produce the same torque Does it follow that they have the same magnitude? Explain
Solution:
No, we know that the torque exerted by a tangential force a distance r from the axis of rotation
is t=rF
Here, the torque depends on both the magnitude of force and on the distance from the axis of rotation at which it is applied However because the forces are the same, the torque depends
on the axis of rotationS A small force can produce the same torque as a large force, if it is applied farther from the axis of rotation

Chapter 11 Rotational Dynamics and Static Equilibrium Q.1P
To tighten a spark plug, it is recommended that a torque of 15 N · m be applied. If a mechanic tightens the spark plug with a wrench that is 25 cm long, what is the minimum force necessary to create the desired torque?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium1ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.2CQ
A car pitches down in front when the brakes are applied sharply. Explain this observation in terms of torques.
Solution:
The torque is given by,t = rF
Here, r is the distance of the axis of rotation to the force and F is the tangential force.
When the brakes are applied, it causes the wheels to lock and then the friction plays the role to stop the car. The total force on the car acts on the center of mass but the friction does not be applied on the center of mass of the vehicle and it is applied to the tires. The friction force opposes the motion and its direction is negative and this causes negative torque to be applied to the vehicle which leads to the clockwise rotation of the center of the mass as given by the expression of the torque. This clockwise rotation of the center of the mass causes the front of the car to pitch downward.
The torque by gravity which is in the opposite direction to the torque by friction acts as the restoring torque because the first law of angular motion states that the body will maintain constant angular motion unless the outside torque is acted upon it. Hence, the car pitches down in front when the brakes are applied sharply.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.2P
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium2p
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.3CQ
A tightrope walker uses a long pole to aid in balancing. Why?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium3cqs

Chapter 11 Rotational Dynamics and Static Equilibrium Q.3P
A 1.61-kg bowling trophy is held at arm’s length, a distance of 0.605 m from the shoulder joint. What torque does the trophy exert about the shoulder if the arm is (a) horizontal, or (b) at an angle of 22.5° below the horizontal?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.4CQ
When a motorcycle accelerates rapidly from a stop it sometimes “pops a wheelie”; that is, its front wheel may lift off the ground. Explain this behavior in terms of torques.
Solution:
The moment of inertia is greatest when more mass is at a greater distance from the axis of rotation. Therefore, rotating the body about an axis through the hips results in the larger moment of inertia. This is true since the angular acceleration is inversely proportional to the moment of inertia. It follows that a given torque produces greater angular acceleration when the body rotates about an axis through the spine.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.4P
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium4p
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.5CQ
Give an example of a system in which the net torque is zero but the net force is nonzero.
Solution:
A force applied radially to a wheel produces zero torque, though the net force is not zero.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.5P
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium5p
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.6CQ
Give an example of a system in which the net force is zero but the net torqueis nonzero.
Solution:
Consider an airplane propeller or a ceiling fan that is just starting to rotate. In both these cases the net force is zero. Here, the center of mass is not accelerating, but the net torque is non-zero.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.6P
At the local playground, a 16-kg child sits on the end of a horizontal teeter-totter, 1.5 m from the pivot point. On the other side of the pivot an adult pushes straight down on the teeter-totter with a force of 95 N. Tn which direction does the teeter-totter rotate if the adult applies the force at a distance of (a) 3.0 m, (b) 2.5 m, or (c) 2.0 m from the pivot?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.7CQ
Is the normal force exerted by the ground the same for all four tires on yourcar? Explain.
Solution:
No, because the engine is situated in front in most of the cars. Thus, most of the car’s mass is located in the front of the car, and the center of mass of the car is not located at the center of the
car. It is closer to the front end. This means that more force is exerted on the front tires than on the back tires. Thus, the normal force applied is equal for all four tires.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.7P
Consider the pulley-block systems shown in Conceptual Checkpoint 11-1. (a) Is the tension in the string on the left-hand rotating system greater than, less than, or equal to the weight of the mass attached to that string? (b) Choose the best explanation from among the following:
I. The mass is in free fall once it is released.
II. The string rotates the pulley in addition to supporting the mass.
III. The mass accelerates downward.
Solution:
a) The mass moves in downward directions. So the tension in the string is less than the weight of the mass.
b) The best option is the mass accelerates downwards.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.8CQ
Give two everyday examples of objects that are not in static equilibrium.
Solution:
(i) A truck accelerating from rest is not in static equilibrium because its center of mass is accelerating.
(ii) An airplane propeller that is just starting up is not in static equilibrium because it has an angular acceleration.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.8P
Consider the pulley-block systems shown in Conceptual Checkpoint 11–1. (a) Is the tension in the string on the left-hand rotating system greater than, less than, or equal to the tension in the string on the right-hand rotating system? (b) Choose the best explanation from among the following:
I. The mass in the right-hand system has the greater downward acceleration.
II. The masses are equal.
III. The mass in the left-hand system has the greater downward acceleration.
Solution:
a) The mass in the left hand system drops with small acceleration than the mass in the right hand system. The tension in the left hand string is greater than the tension in the right hand string.
b) The mass in the left hand mass has smaller acceleration. Option (a) is correct.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.9CQ
Give two everyday examples of objects that are in static equilibrium.
Solution:
Conditions for static equilibrium
(i) The net force acting on the object must be zero.
(ii) The net torque acting on the object must be zero.
The examples that meet these conditions are
(1) A physics text book on the table
(2) A person sitting on the chair

Chapter 11 Rotational Dynamics and Static Equilibrium Q.9P
Suppose a torque rotates your body about one of three different axes of rotation: case A, an axis through your spine; case B, an axis through yorrr hips; and case C, an axis through your ankles. Rank these three axes of rotation in increasing order of the angular acceleration produced by the torque. Indicate ties where appropriate.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium9ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.10CQ
Can an object have zero translational acceleration and, at the same time, have nonzero angular acceleration? if your answer is no, explain why not. If your answer is yes, give a specific example.
Solution:
Yes, an object can have zero translational acceleration with nonzero angular acceleration. An example is a stationary exercise bike, here the wheels do not transport the user anywhere and translational acceleration of the wheels/bike is zero, but through the use of chemical energy the wheels can be rotated faster or slower due to a nonzero angular acceleration.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.10P
A torque of 0.97 N m is applied to a bicycle wheel of radius 35 cm and mass 0.75 kg. Treating the wheel as a hoop, find its angular acceleration.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium10ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.11CQ
Stars form when a large rotating cloud of gas collapses. What happens to the angular speed of the gas cloud as it collapses?
Solution:
When stars are forming, the rotating cloud of gas collapses.
Thus, the radius of rotation decreases.
Therefore, the moment of inertia also decreases. However, we have conservation of angular momentum (L)=lω = constant
Therefore, as I decreases, the angular velocity of the gas cloud increases.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.11P
When a ceiling fan rotating with an angular speed of 2.75 rad/s is turned off, a frictional torque of 0.120 N · m slows it to a stop in 22.5 s. What is the moment of inertia of the fan?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.12CQ
What purpose does the tail rotor on a helicopter serve?
Solution:
The tail rotor on a helicopter has a horizontal axis of rotationi, as opposed to the vertical axis of the main rotor, therefore, the tail rotor produces a horizontal thrust
that tends to rotate the helicopter about a vertical axis. As a result, if the angular speed of the main rotor is increased or decreased. The tail rotor can exert an opposing torque that prevents the entire helicopter from rotating in the opposite direction

Chapter 11 Rotational Dynamics and Static Equilibrium Q.12
When the play button is pressed, a CD accelerates uniformly from, rest to 450 rev/min in 3.0 revolutions. If the CD has a radius of 6.0 cm and a mass of 17 g, what is the torque exerted on it?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.13CQ
Is it possible to change the angular momentum of an object without changing its linear momentum? If your answer is no, explain why not. If your answer is yes, give a specific example.
Solution:
Yes, by keeping its velocity constant. If we change the distances from the axis of rotation r, then we change the angular momentum.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.13P
A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod of length 3.15 m and mass 8.42 kg, find the torque the person must exert on the ladder to give it an angular acceleration of 0.302 rad/s2.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.14CQ
Suppose a diver springs into the air with no initial angular velocity. Can the diver begin to rotate by folding into atucked position? Explain.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium14cqs

Chapter 11 Rotational Dynamics and Static Equilibrium Q.14P
Awheel on a game show is given aninitiai angular speed of 1.22 rad/s. It comes to rest after rotating through 0.75 of a turn. (a) Find the average torque exerted on the wheel given that it is a disk of radius 0.71 m and mass 6.4 kg. (b) If the mass of the wheel is doubled and its radius is halved, will the angle through which it rotates before coming to rest increase, decrease, or stay the same? Explain. (Assume that the average torque exerted on the wheel is unchanged.)
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.15P
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium15p
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.16P
The L-shaped object described in Problem 15 can be rotated in one of the following three ways: case A, about the x axis; case B, about the y axis; and case C, about the z axis (which passes through the origin perpendicular’ to the plane of the figure). If the same torque r is applied in the of these cases, rank them in increasing order of the resulting angular acceleration. Indicate ties where appropriate.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.17P
A motorcycle accelerates from rest, and both the front and rear- tires roll without slipping. (a) Is the force exerted by the ground on the rear tire in the forward or in the backward direction? Explain. (b) Is the force exerted by the ground on the front tire in the forward or in the backward direction? Explain. (c) If the moment of inertia of the front tire is increased, will the motorcycle’s acceleration increase, decrease, or stay the same? Explain.
Solution:
(a) The rear tire rolls forwards such that the force of static friction, opposing motion, points backwards. By Newton’s 3rd law, there is an equal and opposite force, exerted by the ground on the rear tire, pointing forward that counteracts this frictional force.
(b) The front tire rolls forwards such that the force of static friction, opposing motion upon ground contact, points backwards. By Newton’s 3rd law, there is an equal and opposite force, exerted by the ground on the front tire, pointing forward, that counteracts the frictional force.
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.18P
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.19P
A fish takes the bait and pulls on the line with a force of 2.2 N. The fishing reel, which rotates without friction, is a cylinder of radius 0.055 m and mass 0.99 kg. (a) What is the angular acceleration of the fishing reel? (b) How much line does the fish pull from the reel in 0.25 s?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.20P
Repeat the previous problem, only now assume the reel has a friction clutch that exerts a restraining torque of 0.047 N · m.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium20ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.21P
Suppose the person in Active Example 11-3 climbs higher on the ladder. (a) As a result, is the ladder more likely, less likely, or equally likely to slip? (b) Choose the best explanation from among the following:
I. The forces are the same regardless of the person’s position.
II. The magnitude of f 2 must increase as the person moves upward.
III. When the person is higher, the ladder presses down harder on the floor.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.22P
A string that passes over a pulley has a 0.321-kg mass attached to one end and a 0.635-kg mass attached to the other end. The pulley, which is a disk of radius 9.40 cm, has friction in its axle. What is the magnitude of the frictional torque that must be exerted by the axle if the system is to be in static equilibrium?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.23P
To loosen the lid on a jar of jam 8.9 cm in diameter, a torque of 8.5 N · m must be applied to the circumference of the lid. If a jar wrench whose handle extends 15 cm from the center of the jar is attached to the lid, what is the minimum force required to open the jar?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.24P
Consider the system in Active Example 11-1, this time with the axis of rotation at the location of the child. Write out both the condition for zero net force and the condition for zero net torque. Solve for the two forces.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.25P
Referring to the person holding a baseball in Problem 5, suppose the biceps exert just enough upward force to keep the system in static equilibrium. (a) Is the force exerted by the biceps more than, less than, or equal to the combined weight of the forearm, hand, and baseball? Explain. (b) Determine the force exerted by the biceps.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.26P
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Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.27P
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Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.28P
A schoolyard teeter-totter with a total length of 5.2 m and a mass of 38 kg is pivoted at its center. A 19-kg child sits on one end of the teeter-totter. (a) Where should a parent push vertically downward with a force of 210 N in order to hold the teeter-totter level? (b) Where should the parent push with a force of 310 N? (c) How would your answers to parts (a) and (b) change if the mass of the teeter-totter were doubled? Explain.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.29P
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium29p
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.30P
A 0.16-kg meterstick is held perpendicular to avertical wall by a 2.5-m string going from the wall to the far end of the stick. (a) Find the tension in the string. (b) If a shorter string is used, will its tension be greater than, less than, or the same as that found in part (a)? (c) Find the tension in a 2.0-m string.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.31P
Repeat Example 11-4, this time with a uniform diving board that weighs 225 N.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.32P
Babe Ruth steps to the plate and casually points to left center field to indicate the location of his next home run. The mighty Babe holds his bat across his shoulder, with one hand holding the small end of the bat. The bat is horizontal, and the distance from the small end of the bat to the shoulder is 22.5 cm. If the bat has a mass of 1.10 kg and has a center of mass that is 67.0 cm from the small end of the bat, find the magnitude and direction of the force exerted by (a) the hand and (b) the shoulder.
Solution:
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The force exerted by the shoulder on the bat is pointed to the upward direction.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.33P
A uniform metal rod, with a mass of 3.7 kg and a length of 1.2 m, is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.51 m above the base of the rod holds the rod at an angle of 25° above the horizontal. The wire is attached to the top of the rod. (a) Find the tension in the wire. Find (b) the horizontal and (c) the vertical components of the force exerted on the rod by the hinge.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.34P
In the previous problem, suppose the wire is shortened, so that the rod now makes an angle of 35° with the horizontal. The wire is horizontal, as before. (a) Do you expect the tension in the wire to increase, decrease, or stay the same as a result of its new length? Explain. (b) Calculate the tension in the wire.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.35P
Repeat Active Example 11-3, this time with a uniform 7.2-kg ladder that is 4.0 m long.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.36P
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Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.37P
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Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.38P
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Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.39P
A uniform crate with a mass of 16.2 kg rests on a floor with a coefficient of static friction equal to 0.571. The crate is a uniform cube with sides 1.21 m in length. (a) What horizontal force applied to the top of the crate will initiate tipping? (b) If the horizontal force is applied halfway to the top of the crate, it will begin to slip before it tips. Explain.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.40P
In the previous problem, (a) what is the minimum height where the force F can be applied so that the crate begins to tip before sliding? (b) What is the magnitude of the force in this case?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.41P
A hand-held shopping basket 62.0 cm long has a 1.81-kg carton of milk at one end, and a 0.722-kg box of cereal at the other end. Where should a 1.80-kg container of orange juice be placed so that the basket balances at its center?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium41ps

Hence, the orange juice container should be placed from center, on the side of cereal carton, at a distance of.18.5cm

Chapter 11 Rotational Dynamics and Static Equilibrium Q.42P
If the cat in Active Example 11-2 has a mass of 2.8 kg, how close to the right end of the two-by-four can it walle before the board begins to tip?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.43P
A0.34-kg meterstick balances at its center. If a necklace is suspended from one end of the stick, the balance point moves 9.5 cm toward that end. (a) Is the mass of the necklace more than, less than, or the same as that of the meterstick? Explain. (b) Find the mass of the necklace.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.44P
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Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.45P
A baseball bat balances 71.1 cm from one end. If a 0, 560-kg glove is attached to that end, the balance point moves 24.7 cm toward the glove. Find the mass of the bat.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.46P
A 2.85-kg bucket is attached to a disk-shaped pulley of radius 0.121 m and mass 0.742 kg. If the bucket is allowed to fall, (a) what is its linear acceleration? (b) What is the angular acceleration of the pulley? (c) How far does the bucket drop in 1.50 s?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.47P
In the previous problem, (a) is the tension in the rope greater than, less than, or equal to the weight of the bucket? Explain. (b) Calculate the tension in the rope.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.48P
A child exerts a tangential 42.2-N force on the rim of a disk-shaped merry-go-round with a radius of 2.40 m. If the merry-go-round starts at rest and acquires an angular speed of 0.0860 rev/s in 3.50 s, what is its mass?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.49P
You pull downward with a force of 28 N on a rope that passes over a disk-shaped pulley of mass 1.2 kg and radius 0.075 m. The other end of the rope is attached to a 0.67-kg mass. (a) Is the tension in the rope the same on both sides of the pulley? If not, which side has the largest tension? (b) Find the tension in the rope on both sides of the pulley.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.50P
Referring to the previous problem, find the linear acceleration of the 0.67-kg mass.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.51P
A uniform meterstick of mass M has an empty paint can of mass m hangingfrom one end. The meterstick and the can balance at a point 20.0 cm from the end of the stick where the can is attached. When the balanced stick-can system is suspended from a scale, the reading on the scale is 2.54 N. Find the mass of (a) the meterstick and (b) the paint can.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.52P
Atwood’s Machine An Atwood’s machine consists of two masses, m\ and m-i, connected by a string that passes over a pulley. If the pulley is a disk of radius R and mass M, find the acceleration of the masses.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.53P
Calculate the angular momentum of the Earth about its own axis, due to its daily rotation. Assume that the Earth is a uniform sphere.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.54P
A 0.015-kg record with aradiusof!5 cm rotates with an angular speed of rpm. Find the angular momentum of the record.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.55P
Tn the previous problem, a 1.1-g fly lands on the rim of the record. What is the fly’s angular momentum?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.56P
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Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.57P
Repeat the previous problem for the case of jogger 2, whose speed is 2.68 m/s and whose mass is 58.2 kg.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.58P
Suppose jogger 3 in Figure 11-33 has a mass of 62.2 kg and a speed of 5.85 m/s. (a) Is the magnitude of the jogger’s angular momentum greater with respect to point A or point B? Explain. (b) Is the magnitude of the jogger’s angular momentum with respect to point B greater than, less than, or the same as it is with respect to the origin, O?Explain. (c) Calculate the magnitude of the jogger’s angular momentum with respect to points A, B, and O.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.59P
A torque of 0.12 N m is applied to an egg beater. (a) Tf the egg beater starts at rest, what is its angular momentum after 0.65 s? (b) Tf the moment of inertia of the egg beater is 2.5 × 10−3 kg · m2, what is its angular speed after 0.65 s?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.60P
A windmill has an initial angular momentum of 8500 kg · m2 /s. The wind picks up, and 5.86 s later the windmill’s angular momentum is 9700 kg · m2 /s. What was the torque acting on the windmill, assuming it was constant during this time?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.61P
Two gerbils run in place with a linear speed of 0.55 m/s on an exercise wheel that is shaped like a hoop. Find the angular momentum of the system if the gerbil has a mass of 0.22 kg and the exercise wheel has a radius of 9.5 cm and a mass of 5.0 g.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.62P
A student rotates on a frictionless piano stool with his arms outstretched, a heavy weight in the hand. Suddenly he lets go of the weights, and they fall to the floor. As a result, does the student’s angular speed increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The loss of angular momentum when the weights are dropped causes the student to rotate more slowly.
II. The student’s moment of inertia is decreased by dropping the weights.
III. Dropping the weights exerts no torque on the student, but the floor exerts a torque on the weights when they land.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.63P
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.64P
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.65P
As an ice skater begins a spin, his angular speed is 3.17 rad/s. After pulling in Ms arms, his angular speed increases to 5.46 rad/s. Find the ratio of the skater’sfinalmoment of inertia to his initial moment of inertia.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.66P
Calculate both the initial and the final kinetic energies of the system described in Active Example 11-5.
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.67P
A diver tucks her body in midnight, decreasing her moment of inertia by a factor of two. By what factor does her angular speed change?
Solution:
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Chapter 11 Rotational Dynamics and Static Equilibrium Q.68P
In the previous problem, (a) does the diver’s kinetic energy increase, decrease, or stay the same? (b) Calculate the ratio of the final kinetic energy to the initial kinetic energy for the diver.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium68ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.69P
A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg rotates freely with an angular speed of 0, 641 rev/s. A 59.4-kg person running tangential to the rim of the merry-go-round at 3.41 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round’s rim. What is the final angidar speed of the merry-go-round?
Solution:
Mass of the merry-go-round (M) = 155 kg
Radius of the merry-go-round (R) = 2.63 m
Initial angular speed of the merry-go-round
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium69ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.70P
In the previous problem, (a) does the kinetic energy of the system increase, decrease, or stay the same when the person jumps on the merry-go-round? (b) Calculate the initial and final kinetic energies for this system.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium70ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.71P
A student sits at rest on a piano stool tha t can rotate without friction. The moment of inertia of the student-stool system is 4.1 kg · m2. A second student tosses a 1.5-kg mass with a speed of 2.7 m/s to the student on the stool, who catches it at a distance of 0.40 m from the axis of rotation. What is the resulting angular speed of the student and the stool?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium71ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.72P
Referring to the previous problem, (a) does the kinetic energy of the mass-student-stool system increase, decrease, or stay the same as the mass is caught? (b) Calculate the initial and final kinetic energies of the system.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium72ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.73P
A turntable with a moment of inertia of 5.4 × 10 −3 kg-m2 rotates freely with an angular speed of rpm. Riding on the rim of the turntable, 15 cm from the center, is a cute, 32-g mouse. (a) if the mouse walks to the center of the turntable, will the turntable rotate faster, slower, or at the same rate? Explain. (b) Calculate the angular speed of the turntable when the mouse rthees the center.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium73ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.74P
A student on a piano stool rotates freely with an angular speed of 2.95 rev/s. The student holds a 1.25-kg mass in the outstretched arm, 0.759 m from the axis of rotation. The combined moment of inertia of the student and the stool, ignoring the two masses, is 5.43 kg -m2, a value that remains constant. (a) As the student pulls his arms inward, his angular speed increases to 3.54 rcv/s. How farare the masses from the axis of rotation at this time, considering the masses to be points? (b) Calculate the initial and final kinetic energies of the system.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium74ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.75P
A child of mass m tands at rest near the rim of a stationary merry-go-round of radius R and moment of inertia I. The child now begins to walk around the circumference of the merry-go-round with a tangential speed v with respect to the merry-go-round’s surface. (a) What is the child’s speed with respect to the ground? Check your results in the limits (b) I → 0 and (c) I →∞
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium75ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.76P
Two spheres of equal mass and radius are rolling across the floor with the same speed. Sphere 1 is a uniform solid; sphere 2 is hollow. Is the work required to stop sphere 1 greater than, less than, or equal to the work required to stop sphere 2? (b) Choose the best explanation from among the following:
I. Sphere 2 has the greater moment of inertia and hence the greater rotational kinetic energy.
II. The spheres have equal mass and speed; therefore, they have the same kinetic energy.
III. The hollow sphere has less kinetic energy.
Solution:
The mass, radius and speed of the both balls are same. The kinetic energy of the hallow sphere is more than the kinetic energy of the sold sphere. According to work energy theorem, the work done would be greater for ball that posses more kinetic energy. So Work required to stop sphere1 is less than the work done to stop sphere2. The moment of inertia of the of the hallow ball is greater and hence the greater rotational kinetic energy.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.77P
How much work must be done to accelerate a baton from rest to an angular speed of 7.4 rad/s about its center? Consider the baton to be a uniform rod of length 0.53 m and mass 0.44 kg.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium77ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.78P
Turning a doorknob through. 0.25 of a revolution requires 0.14 J of work. What is the torque required to turn the doorknob?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium78ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.79P
A person exerts a tangential force of 36.1 N on the rim of a disk-shaped merry-go-round of radius 2.74 m and mass 167 kg. If the merry-go-round starts at rest, what is its angular speed after the person has rotated it through an angle of 32.5°?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium79ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.80P
To prepare homemade ice cream, a crank must be turned with a torque of 3.95 N· m. How much work is required for the complete turn of the crank?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium80ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.81P
A popular make of dental drill can operate at a speed of 42, 500 rpm while producing a torque of 3.68 oz · in. What is the power output of this drill? Give your answer in watts.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium81ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.82P
The L-shaped object in Figure 11-24 consists of three masses connected by light rods. Find the work that must be done on this object to accelerate it from rest to an angular speed of 2.35 rad/s about (a) the x axis, (b) the y axis, and (c) the z axis (which is through the origin and perpendicular to the page).
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium82ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.83P
The rectangular object in Figure 11-25 consists of four masses connected by light rods. What power must be applied to this object to accelerate it from rest to an angular speed of 2.5 rad/s in 6.4 s about (a) the x axis, (b) the y axis, and (c) the z axis (which is through the origin and perpendicular to the page)?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium83ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.84P
A circular saw blade accelerates from rest to an angular speed of 3620 rpm in 6.30 revolutions. (a) Find the torque exerted on the saw blade, assuming it is a disk of radius 15.2 cm and mass 0.755 kg. (b) Is the angular speed of the saw blade after 3.15 revolutions greater than, less than, or equal to 1810 rpm? Explain. (c) Find the angular speed of the blade after 3.15 revolutions.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium84ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.85GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium85p
Solution:
a) From the given figure, if the paper is pulled horizontally to the right, then the disk rotates in a counterclockwise direction because the force is exerted to the right on the bottom of the disk.
b) The center of the disk moves toward the right because the paper is pulled to the right. This is the direction of the net force exerted on the disk.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.86GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium86p
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.87GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium87p
Solution:
(a) When the block is allowed to fall, the block moves towards the left.
(b) The wheel has larger moment of inertia and smaller angular acceleration. Therefore the string unwinds from the wheel more slowly than the disk, and so the block moves to the left.
Option (II) is correct.

Chapter 11 Rotational Dynamics and Static Equilibrium Q.88GP
A beetle sits at the rim of a turntable that is at rest but is free to rotate about a vertical axis. Suppose the beetle now begins to walk around the perimeter of the turntable. Does the beetle move forward, backward, or does it remain in the same location relative to the ground? Answer for two different cases, (a) the turntable is much more massive than the beetle and (b) the turntable is massless.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium88ps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.89GP
A beetle sits near the rim of a turntable that is rotating without friction about a vertical axis. The beetle now begins to walk toward the center of the turntable. As a result, does the angular speed of the turntable increase, decrease, or stay the same? Explain.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium89gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.90GP
Suppose the Earth were to magically expand, doubling its radius while keeping its mass the same. Would the length of the day increase, decrease, or stay the same? Explain.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium90gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.91GP
After getting a drink of water, a hamster jumps onto an exercise wheel for a run. A few seconds later the hamster is running in place with a speed of 1, 3 m/s. Find the work done by the hamster to get the exercise wheel moving, assuming it is a hoop of radius 0.13 m and mass 6.5 g.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium91gp

Chapter 11 Rotational Dynamics and Static Equilibrium Q.92GP
A 47.0-kg unif orm rod 4.25 m long is attached to a wall with a hinge at one end. The rod is held in a horizontal position by, a wire attached to its other end. The wire makes an angle of 30.0° with the horizontal, and is bolted to the wall directly above the hinge. If the wire can withstand a maximum tension of 1450 N before breaking, how far from the wall can a 68.0-kg person sit without breaking the wire?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium92gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.93GP
A puck attached to a string moves in a circular path on a frictionless surface, as shown in Figure 11–34. Initially, the speed of the puck is v and the radius of the circle is r. If the string passes through ahole in the surface, and is pulled downward until the radius of the eircularpath is r /2, (a) does the speed of the puck increase, decrease, or stay the same? (b) Calculate the final speed of the puck.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium93gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.94GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium94gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.95GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium95gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.96GP
Auto mechanics use the following formula to calculate the horsepower (HP) of a car engine: In this expression, Torque is the torque produced by the engine in ft · lb, RPM is the angular speed of the engine in revolutions per minute, and C is a dimensionless constant. (a) Find the numerical value of C. (b) The Shelby Series 1 engine is advertised to generate 320 hp at 6500 rpm. What is the corresponding torque produced by this engine? Give your answer in ft · lb.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium96gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.97GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium97gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.98GP
You hold a uniform, 28-g pen horizontal with your thumb pushing down on one end and your index finger pushing upward 3.5 cm from, your thumb. The pen is 14 cm long. (a) Which of these two forces is greater in magnitude? (b) Find the two forces.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium98gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.99GP
In Active Example 11-3, suppose the ladder is uniform, 4.0 m long, and weighs 60.0 N. Find the forces exerted on the ladder when the person is (a) halfway up the ladder and (b) three-fourths of the way up the ladder.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium99gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.100GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium100gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.101GP
A 67, 0-kg person stands on a lightweight diving board supported by two pillars, one at the end of the board, the other 1.10 m away. The pillar at the end of the board exerts a downward force of 828 N. (a) How far from that pillar is the person standing? (b) Find the force exerted by the second pillar.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium101gps

Therefore, the force exerted by the second pillar is.1.49KN

Chapter 11 Rotational Dynamics and Static Equilibrium Q.102GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium102gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.103GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium103gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.104GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium104gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.105GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium105gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.106GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium106gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.107GP
Suppose a fourth book, the same as the other three, is added to the stack of books shown in Figure 11-32. (a) What is the maximum overhang distance, d, in this case? (b) If the mass of the book is increased by the same amount, does your answer to part (a) increase, decrease, or stay the same? Explain.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium107gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.108GP
Suppose partial melting of the polar ice caps increases the moment of inertia of the Earth from 0.331 M E R E 2 to 0.332 M E R E 2. (a) Would the length of a day (the time required for the Earth to complete one revolution about its axis) increase or decrease? Explain. (b) Calculate the change in the length of a day. Give your answer in seconds.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium108gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.109GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium109gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.110GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium110gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.111GP
In Problem, assume that the rod has a mass of M and that its bottom end simply rests on the floor, held in place by static friction. If the coefficient of static friction is μs, find the maximum force F that can be applied to the rod at its midpoint before it slips.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium111gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.112GP
In the previous problem, suppose the rod has a mass of 2.3 kg and the coefficient of static friction is 1/7. (a) Find the greatest force F that can be applied at the midpoint of the rod without causing it to slip. (b) Show that if F is applied 1/8 of the way down from the top of the rod, it will never slip at all, no matter how large the force F.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium112gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.113GP
A cylinder of mass m and radius r has a string wrapped around its circumference. The upper end of the string is held fixed, and the cylinder is allowed to fall. Show that its linear acceleration is (2/3)g.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium113gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.114GP
Repeat the previous problem, replacing the cylinder with a solid sphere. Show that its linear acceleration is (5/7)g.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium114gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.115GP
A mass M is attached to a rope that passes over a disk-shaped pulley of mass m and radius r. The mass hangs to the left side of the pulley. On the right side of the pulley, the rope is pulled downward with a force F. Find (a) the acceleration of the mass, (b) the tension in the rope on the left side of the pulley, and (c) the tension in the rope on the right side of the pulley, (d) Check your results in the limits m → 0 and m →∞.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium115gps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.116GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium116gp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.117GP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium117pp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.118PP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium118pp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.119PP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium119pp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.120PP
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium120pp
Solution:

Chapter 11 Rotational Dynamics and Static Equilibrium Q.121IP
Suppose the mass of the pulley is doubled, to 0.160 kg, and that everything else in the system remains the same. (a) Do you expect the value of T 2 to increase, decrease, or stay the same? Explain, (b) Calculate the value of T 2 for this case.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium121pps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.122IP
Suppose the mass of the cart is doubled, to 0.62 kg, and that everything else in the system remains the same. (a) Do you expect the value of T 2 to increase decrease, or stay the same? Explain. (b) Calculate the value of T 2 for this case.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium122pps

Chapter 11 Rotational Dynamics and Static Equilibrium Q.123IP
Suppose the child runs with a different initial speed, but that everything else in the system remains the same. What initial speed does the child have if the angular speed of the system after the collision is 0.425 rad/s?
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium123ips

Chapter 11 Rotational Dynamics and Static Equilibrium Q.124IP
Suppose everything in the system is as described in Active Example 11-5 except that the child approaches the merry-go-round in a direction that is not tangential Find the angle θ between the direction of motion and the outward radial direction (as in Example 11-8) that is required if the final angular speed of the system is to be 0.272 rad/s.
Solution:
Mastering Physics Solutions Chapter 11 Rotational Dynamics and Static Equilibrium124ips

Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy

May 26, 2018May 26, 2018 by Prasanna

Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy

Mastering Physics Solutions

Chapter 10 Rotational Kinematics and Energy Q.1CQ
A rigid object rotates about a fixed axis Do all points on the object have the same angular speed? Do all points on the object have the same linear speed? Explain
Solution:
Yes, all points on the rigid object have the same angular speed. but the linear speed is not the same at all points The linear speed near the point of the axis of rotation will be lower relative to
points further away from the axis of rotation Thus, it can be increased by increasing the distance away from the axis of rotation (v =r ω)

Chapter 10 Rotational Kinematics and Energy Q.1P
The following angles are given in degrees. Convert them to radians: 30°, 45°, 90°, 180°.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy1ps

Chapter 10 Rotational Kinematics and Energy Q.2CQ
Can you drive your car in such a way that your tangential acceleration is zero while at the same time your centripetal acceleration is nonzero? Give an example if your answer is yes. state why not if your answer is no.
Solution:
Yes Tangential acceleration is caused by a changing tangential speed. while centripetal acceleration is caused by a changing direction of motion. If you drive a car in a circular path with constant speed. tangential acceleration is zero while centripetal acceleration is non-zero

Chapter 10 Rotational Kinematics and Energy Q.2P
The following angles are given in radians. Convert them to degrees: π/6, 0.70π, 1.5π, 5π.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy2ps

Chapter 10 Rotational Kinematics and Energy Q.3CQ
Can you drive your car in such a way that your tangential acceleration is nonzero while at the same time your centripetal acceleration is zero? Give an example if your answer is yes. state why not if your answer is no.
Solution:
If you are traveling in a circular path. your centripetal acceleration is always non zero So it is not possible to have zero centripetal acceleration If you are traveling in a straight path. the centripetal acceleration does not arise at all So it is not relevant

Chapter 10 Rotational Kinematics and Energy Q.3P
Find the angular speed of (a) the minute hand and (b) the hour hand of the famous clock in London, England, that rings the bell known as Big Ben.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy3ps

Chapter 10 Rotational Kinematics and Energy Q.4CQ
The fact that the Earth rotates gives people in New York a linear speed of about 750 mi/hrn Where should you stand on the Earth to have the smallest possible linear speed?
Solution:
We should stand on Earth’s poles for the smallest possible linear speed (v) This is because Earth has a constant angular speed. and the distance from the axis of rotation at the poles is the smallest compared to other places on Earth (v =r ω)

Chapter 10 Rotational Kinematics and Energy Q.4P
Express the angular velocity of the second hand on a clock in trie following units: (a) rev/hr, (b) deg/min, and (c) rad/s.
Solution:
Time taken by the second hand to complete one revolution(T) = 60s=1min
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy4ps

Chapter 10 Rotational Kinematics and Energy Q.5CQ
At the local carnival you and a friend decide to take a ride on the Ferris wheel. As the wheel rotates with a constant angular speed, your friend poses the following questions: (a) is my linear velocity constant? (b) Is my linear speed constant? (c) is the magnitude of my centripetal acceleration constant? (d) Is the direction of my centripetal acceleration constant? What is your answer to each of these questions?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy5cqs

Chapter 10 Rotational Kinematics and Energy Q.5P
Rank the following inorder of increasing angular speed: an automobile tire rotating at 2.00 × 103 deg/s, an electric drill rotating at 400.0 rev/min, and an airplane propeller rotating at 40.0 rad/s.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy5ps

Chapter 10 Rotational Kinematics and Energy Q.6CQ
Why should changing the axis of rotation of an object change its moment of inertia, given that its shape and mass remain the same?
Solution:
We know that the moment of inertia of an object depends on its mass, shape. and siz4 By changing the axis of rotation, the size of the object will also change (distance from the axis of rotation) Therefore, the moment of inertia of the object changes

Chapter 10 Rotational Kinematics and Energy Q.6P
A spot of paint on a bicycle tire moves in a circular path of radius 0.33 m. When the spot has traveled a linear distance of 1.95 m, through what angle has the tire rotated? Give your answer in radians.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy6ps

Chapter 10 Rotational Kinematics and Energy Q.7CQ
Give a common, everyday example for each of the following: (a) An object that has zero rotational kinetic energy but nonzero translational kinetic energy. (b) An object that has zero translational kinetic energy but nonzero rotational kinetic energy. (c) An object that has nonzero rotational and translational kinetic energies.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy7cqps

Chapter 10 Rotational Kinematics and Energy Q.7P
What is the angular speed (in rev/min) of the Earth as it orbits about the Sun?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy7ps

Chapter 10 Rotational Kinematics and Energy Q.8CQ
Two spheres have identical radii and masses. How might you tell which of these spheres is hollow and which is solid?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy8cqs

Chapter 10 Rotational Kinematics and Energy Q.8P
Find the angular speed of the Earth as it spins about its axis. Give your result in rad/s.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy8ps

Chapter 10 Rotational Kinematics and Energy Q.9CQ
At the grocery store you pick up a can of beef broth and a can of chunky beef stew. The cans are identical in diameter and. weight. Rolling both of them down the aisle with the same initial speed, you notice that the can of chunky stew rolls much farther than the can of broth. Why?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy9cqs

Chapter 10 Rotational Kinematics and Energy Q.9P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy9p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.10CQ
Suppose we change the race shown in Conceptual Checkpoint 10-4 so that a hoop of radius R and mass M races a hoop of radius R and mass 2M. (a) Does the hoop with mass M finish before, after, or at the same time as the hoop with mass 2M? Explain. (b) How would your answer to part (a) change if the hoops had different radii? Explain.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy10cqs

Chapter 10 Rotational Kinematics and Energy Q.10P
A 3.5-inch floppy disk in a computer rotates with a period of 2.00 × 10− 1 s. What are (a) the angular speed of the disk and (b) the linear speed of a point on the rim of the disk? (c) Does a point near the center of the disk have an angular speed that is greater than, less than, or the same as the angular speed found in part (a)? Explain. (Note: A 3.5-inch floppy disk is 3.5 inches in diameter.)
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy10ps

Chapter 10 Rotational Kinematics and Energy Q.11P
The angle an airplane propeller makes with the horizontal as a function of time is given by θ = (125 rad/s)t + (42.5 rad/s2)t 2. (a) Estimate the instantaneous angular velocity at t = 0.00 s by calculating the average angular velocity from t = 0.00 s to t = 0.010 s. (b) Estimate the instantaneous angular velocity at t − 1.000 s by calculating the average angular velocity from t = 1.000 s to t = 1.010 s. (c) Estimate the instantaneous angular velocity at t = 2.000 s by calculating the average angular velocity from t = 2.000 s to t = 2.010 s. (d) Based on your results from parts (a), (b), and (c), is the angular acceleration of the propeller positive, negative, or zero? Explain. (e) Calculate the average angular acceleration from t = 0.00 s to t − 1.00 s and from t = 1.00 s to t = 2.00 s.
SECTION 10-2 ROTATIONAL KINEMATICS
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy11ps

Chapter 10 Rotational Kinematics and Energy Q.12
An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θ in the time t, through what angle did it rotate in the time t /2?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy12ps

Chapter 10 Rotational Kinematics and Energy Q.13P
An object at rest begins to rotate with a constant angular acceleration. If the angular speed of the object is w after the time t, what was its angular speed at the time t /2?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy13ps

Chapter 10 Rotational Kinematics and Energy Q.14P
In Active Example, how long does it take before the angular velocity of the pulley is equal to −5.0 rad/s?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy14ps

Chapter 10 Rotational Kinematics and Energy Q.15P
In Example, through what angle has the wheel turned when its angular speed is 2.45 rad/s?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy15ps

Chapter 10 Rotational Kinematics and Energy Q.16P
The angular speed of a propeller on a boat increases with constant acceleration from 12 rad/s to 26 rad/s in 2.5 revolutions. What is the acceleration of the propeller?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy16ps

Chapter 10 Rotational Kinematics and Energy Q.17P
The angular speed of a propeller on a boat increases with constant acceleration from 11 rad/s to 28 rad/s in 2.4 seconds. Through what angle did the propeller turn during this time?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy17ps

Chapter 10 Rotational Kinematics and Energy Q.18P
After fixing a flat tire on a bicycle you give the wheel a spin. (a) If its initial angular speed was 6.35 rad/s and it rotated 14.2 revolutions before coming to rest, what was its average angular acceleration? (b) For what length of time did the wheel rotate?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy18ps

Chapter 10 Rotational Kinematics and Energy Q.19P
A ceiling fan is rotating at 0.96 rev/s. When turned off, it slows uniformly to a stop in2.4 min. (a) How many revolutions does the fan make in this time? (b) Using the result from part (a), find the number of revolutions the fan must make for its speed to decrease from 0.96 rev/s to 0.48 rev/s.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy19ps

Chapter 10 Rotational Kinematics and Energy Q.20P
A discus thrower starts from rest and begins to rotate with a constant angular acceleration of 2.2 rad/s2, (a) How many revolutions does it take for the discus thrower’s angular speed to rthe 6.3 rad/s? (b) How much time does this take?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy20ps

Chapter 10 Rotational Kinematics and Energy Q.21P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy21p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.22P
A centrifuge is a common laboratory instrument that separates components of differing densities in solution. This is accomplished by spinning a sample around in a circle with a large angular speed. Suppose that after a centrifuge in a medical laboratory is turned off, it continues to rotate with a constant angular deceleration for 10.2 s before coming to rest. (a) If its initial angular speed was 3850 rpm, what is the magnitude of its angular deceleration? (b) How many revolutions did the centrifuge complete after being turned off?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy22ps

Chapter 10 Rotational Kinematics and Energy Q.23P
The Earth’s rate of rotation is constantly decreasing, causing the day to increase in duration. In the year 2006 the Earth took about 0.840 s longer to complete 365 revolutions than it did in the year 1906. What was the average angular acceleration of the Earth during this time? Give your answer in rad/s.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy23ps

Chapter 10 Rotational Kinematics and Energy Q.24P
A compact disk (CD) speeds up uniformly from rest to 310 rpm in 3.3 s. (a) Déscribe a strategy that allows you to calculate the number of revolutions the CD makes in this time. (b) Use your strategy to find the number of revolutions.
Solution:
a) The CD moves speeds up with uniform velocity. Initially we determine the angular acceleration to determine the angular displacement.
b) The angular acceleration of the compact disc which speeds up uniformly is given from the equation 10-8 is
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy24ps

Chapter 10 Rotational Kinematics and Energy Q.25P
When a carpenter shuts off his circular saw, the 10.0-inch-diameter blade slows from 4440 rpm to 0.00 rpm in 2.50 s. (a) What is the angular acceleration of the blade? (b) What is the distance traveled by a point on the rim of the blade during the deceleration? (c) What is the magnitude of the net displacement of a point on the rim of the blade during the deceleration?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy25ps

Chapter 10 Rotational Kinematics and Energy Q.26P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy26p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.27P
Two children, Jason and Betsy, ride on the same merry-go-round. Jason is a distance R from, the axis of rotation; Betsy is a distance 2R from the axis. Is the rotational period of Jason greater than, less than, or equal to the rotational period of Betsy? (b) Choose the best explanation from among the following:
I. The period is greater for Jason because he moves more slowly than Betsy.
II. The period is greater for Betsy since she must go around a circle with a larger circumference.
III. It takes the same amount of time for the merry-go-round to complete a revolution for all points on the merry-go-round.
Solution:
a) The rotational period of Jason is equal to the rotational period of Betsy.
b) The angular speed of the merry go round is constant and the period is constant for every point on it. So option III is correct explanation.

Chapter 10 Rotational Kinematics and Energy Q.28P
Referring to the previous problem, what are (a) the ratio of Jason’s angular speed to Betsy’s angular speed, (b) the ratio of Jason’s linear speed to Betsy’s linear speed, and (c) the ratio of Jason’s centripetal acceleration to Betsy’s centripetal acceleration?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy28ps

Chapter 10 Rotational Kinematics and Energy Q.29P
The world’s tallest building is the Taipei 101 Tower in Taiwan, which rises to a height of 508 m (1667 ft). (a) When standing on the top floor of the building, is your angular speed due to the Earth’s rotation greater than, less than, or equal to your angular speed when you stand on the ground floor? (b) Choose the best explanation from among the following;
I. The angular speed is the same at all distances from the axis of rotation.
II. At the top of the building you are farther from the axis of rotation and hence you have a greater angular speed.
III. You are spinning faster when you are closer to the axis of rotation.
Solution:
a) The angular speed of the earth rotation is equal.
b) Our angular speed due to Earth’s rotation is same at every point on the earth irrespective of the elevation. So your angular speed due to earth’s rotation on the top floor of the building will be same as it is on the ground floor. Option I is correct.

Chapter 10 Rotational Kinematics and Energy Q.30P
The hour hand on a certain clock is 8.2 cm long, Find the tangential speed of the tip of this hand.
Solution:
The tangential speed in case of circular motion is, v =rω Here, r represents radius and ω represents angular velocity.
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy30ps

Chapter 10 Rotational Kinematics and Energy Q.31P
Two children ride on the merry-go-round shown in Conceptual Checkpoint 10-1. Child 1 is 2.0 m from the axis of rotation, and child 2 is 1.5 m from the axis. If the merry-go-round completes one revolution every 4.5 s, find (a) the angular speed and (b) the linear speed of the child,
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy31ps

Chapter 10 Rotational Kinematics and Energy Q.32P
The outer edge of a rotating Frisbee with a diameter of 29 cm has a linear speed of 3.7 m/s. What is the angular speed of the Frisbee?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy32ps

Chapter 10 Rotational Kinematics and Energy Q.33P
A carousel at the local carnival rotates once every 45 seconds. (a) What is the linear speed of an outer horse on the carousel, which is 2.75 m from the axis of rotation? (b) What is the linear speed of an inner horse that is 1.75 m from the axis of rotation?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy33ps

Chapter 10 Rotational Kinematics and Energy Q.34P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy34p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.35P
Suppose, in Problem 34, that at some point inhis swing Jeff of the Jungle has an angular speed of 0.850 rad/s and an angular acceleration of 0.620 rad/s2. Find the magnitude of his centripetal, tangential, and total accelerations, and the angle his total acceleration makes with respect to the tangential direction of motion.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy35ps

Chapter 10 Rotational Kinematics and Energy Q.36P
A compact disk, which has a diameter of 12.0 cm, speeds up uniformly from 0.00 to 4.00 rev/s in 3.00 s. What is the tangential acceleration of a point on the outer rim of the disk at the moment when its angular speed is (a) 2.00 rev/s and (b) 3.00 rev/s?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy36ps

Chapter 10 Rotational Kinematics and Energy Q.37P
When a compact disk with a 12.0-cm diameter is rotating at 5.05 rad/s, what are (a) the linear speed and (b) the centripetal acceleration of a point on its outer rim? (c) Consider a point on the CD that is halfway between its center and its outer rim. Without repeating all of the calculations required for parts (a) and (b), determine the linear speed and the centripetal acceleration of this point.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy37ps

Chapter 10 Rotational Kinematics and Energy Q.38P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy38p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.39P
A Ferris wheel with a radius of 9.5 rotates a constant rate, completing one revolution every 36 second. Find the direction and a passenger’s acceleration when (a) at the top and (b) at the bottom of the wheel.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy39ps
Chapter 10 Rotational Kinematics and Energy Q.40P
Suppose the Ferris wheel in the previous problem begins to decelerate at the rate of 0.22 rad/s2 when the passenger is at the top of the wheel. Find the direction and magnitude of the passenger’s acceleration at that time.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy40ps

Chapter 10 Rotational Kinematics and Energy Q.41P
A person swings a 0.52-kg tether ball tied to a 4.5-m rope in an approximately horizontal circle. (a) If the maximum tension the rope can withstand before breaking is 11 N, what is the maximum angular speed of the ball? (b) If the rope is shortened, doea the maximum angular speed found in part (a) increase, decrease, or stay the same? Explain.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy41ps

Chapter 10 Rotational Kinematics and Energy Q.42P
To polish a filling, a dentist attaches a sanding disk with a radius of 3.20 mm to the drill. (a) When the drill is operated at 2.15 × 104 rad/s, what is the tangential speed of the rim of the disk? (b) What period of rotation must the disk have if the tangential speed of its rim is to be 275 m/s?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy42ps

Chapter 10 Rotational Kinematics and Energy Q.43P
In the previous problem, suppose the disk has an angular acceleration of 232 rad/s2 when its angular speed is 640 rad/s. Find both the tangential and centripetal accelerations of a point on the rim of the disk.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy43ps

Chapter 10 Rotational Kinematics and Energy Q.44P
The Bohr model of the hydrogen atom pictures the electron as a tiny particle moving in a circular orbit about a stationary proton. In the lowest-energy orbitthe distance from the proton to the electron is 5.29 × 10−11 m, and die linear speed of the electron is 2. 18 × 106 m/s. (a) What is the angular speed of the electron? (b) How many orbits about the proton does it make the second? (c) What is the electron’s centripetal acceleration?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy44ps

Chapter 10 Rotational Kinematics and Energy Q.45P
A wheel of radius R starts from rest and accelerates with a constant angular acceleration x about a fixed axis. At what time t will the centripetal and tangential accelerations of a point on the rim have the same magnitude?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy45ps

Chapter 10 Rotational Kinematics and Energy Q.46P
As you drive down the highway, the top of your tires are moving with a speed v. What is the reading on your speedometer?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy46ps

Chapter 10 Rotational Kinematics and Energy Q.47P
The tires on a car have a radius of 31 cm. What is the angular speed of these tires when the car is driven at 15 m/s?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy47ps

Chapter 10 Rotational Kinematics and Energy Q.48P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy48p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.49P
A soccer ball, which has a circumference of 70.0 cm, rolls 14.0 yards in 3.35 s. What was the average angular speed of the ball during this time?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy49ps

Chapter 10 Rotational Kinematics and Energy Q.50P
As you drive down the road at 17 m/s, you press on the gas pedal and speed up with a uniform acceleration of 1, 12 m/s2 for 0.65 s. if the tires on your car have a radius of 33 cm, what is their angular displacement during this period of acceleration?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy50ps

Chapter 10 Rotational Kinematics and Energy Q.51P
A bicycle coasts downhilland accelerates from rest to a linear speed of 8.90 m/s in 12.2 s. (a) If the bicyde’stires have a radius of 36.0 cm, what is theirangular accelerator? (b) If the radius of the tires had been smaller, would their angular acceleration be greater than or less than the result found in part (a)
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy51ps

Chapter 10 Rotational Kinematics and Energy Q.52P
The minute and hour hands of a clock have a common axis of rotation and equal mass. The minute hand is long, thin, and uniform; the hour hand is short, thick, and uniform. (a) Is the moment of inertia of the minute hand greater than, less than, or equal to the moment of inertia of the hour hand? (b) Choose the best explanation from among the following:
I. The hands have equal mass, and hence equal moments of inertia.
II. Having mass farther from the axis of rotation results in a greater moment of inertia.
III. The more compact hour hand concentrates its mass ared has the greater moment of inertia.
Solution:
a) The moment of inertia depends on mass and radius of the body. As the mass of the hour hand and minutes hand are same, the moment of inertia depends on the length of the hand. The length of the minutes hand is greater than the hour’s hand, so moment of inertia of minutes hand is greater than the hour hand.
b) The mass farther from the axis of rotation results in greater moment of inertia.

Chapter 10 Rotational Kinematics and Energy Q.53P
Tons of dust and small particles rain down onto the Earth from space every day. As a result, does the Earth’s moment of inertia increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The dust adds mass to the Earth and increases its radius slightly.
II. As the dust moves closer to the axis of rotation, the moment of inertia decreases.
III. The moment of inertia is a conserved quantity and cannot change.
Solution:
a) Moment of inertia depends upon the mass and radius of the earth. As dust and small particles add up with increase in radius, moment of inertia increases.
b) The moment of inertia of earth, increase because both the mass and radius of earth increased.(I α mr2) Option I is correct.

Chapter 10 Rotational Kinematics and Energy Q.54P
Suppose a bicycle wheel is rotated about an axis through its rim and parallel to its axle. (a) Is its moment of inertia about this axis greater than, less than, or equal to its moment of inertia about its axle? (b) Choose the best explanation from among the following:
I. The moment of inertia is greatest when an object is rotated about its center.
II. The mass and shape of the wheel remain the same.
III. Mass is farther from the axis when the wheel is rotated about the rim.
Solution:
a) Moment of inertia about the rim of the wheel is greater than the moment of inertia about the axle.
b) Moment of inertia is greater when the mass is farther from the axis when the wheel is rotating about the rim.

Chapter 10 Rotational Kinematics and Energy Q.55P
The moment of inertia of a 0.98-kg bicycle wheel rotating about its center is 0.13 kg · m 2. What is the radius of this wheel, assuming the weight of the spokes can be ignored?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy55ps

Chapter 10 Rotational Kinematics and Energy Q.56P
What is the kinetic energy of the grindstone inExample 10-4 if it completes one revolution every 4.20 s?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy56ps

Chapter 10 Rotational Kinematics and Energy Q.57P
An electric fan spinning with an angular speed of 13 rad/s has a kinetic energy of 4.6 J. What is the moment of inertia of the fan?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy57ps

Chapter 10 Rotational Kinematics and Energy Q.58P
Repeat Example 10-5 for the case of a rolling hoop of the same mass and radius.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy58ps

Chapter 10 Rotational Kinematics and Energy Q.59P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy59p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.60P
A 12-g CD with a radius of 6.0 cm rotates with an angular speed of 34 rad/s. (a) What is its kinetic energy? (b) What angularspeed must the CD have if its kinetic energy is to be doubled?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy60ps

Chapter 10 Rotational Kinematics and Energy Q.61P
When a pitcher throws a curve ball, the ball is given a fairly rapid spin. If a 0.15-kg baseball with a radius of 3.7 cm is thrown with a linear speed of 48 m/s and an angular speed of 42 rad/s, how much of its kinetic energy is translational and how much is rotational? Assume the ball is a uniform, solid sphere.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy61ps

Chapter 10 Rotational Kinematics and Energy Q.62P
A basketball rolls along the floor with a constant linear speed v. (a) Find the fraction of its total kinetic energy that is in the form of rotational kinetic energy about the center of the ball. (b) If the linear speed of the ball is doubled to 2v, does your answer to part (a) increase, decrease, or stay the same? Explain.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy62ps

Chapter 10 Rotational Kinematics and Energy Q.63P
Find the rate at which the rotational kinetic energy of the Earth is decreasing. The Earth has a moment of inertia of 0.331M e R e 2 where R E = 6.38 × 106 m and M E = 5.97 × 1024 kg, and its rotational period increases by 2.3 ms with the passing century. Give your answer in watts.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy63ps

Chapter 10 Rotational Kinematics and Energy Q.64P
A lawn mower has a flat, rod-shaped steel blade that rotates about its center. The mass of the blade is 0.65 kg and its length is 0.55 m. (a) What is the rotational energy of the blade at its operating angular speed of 3500 rpm? (b) If all of the rotational kinetic energy of the blade could be converted to gravitational potential energy, to what height would the blade rise?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy64ps

Chapter 10 Rotational Kinematics and Energy Q.65P
Consider the physical situation shown in Conceptual Checkpoint 10-5. Suppose this time a ball is released from rest on the frictionless surface. When the ball comes to rest on the no-slip surface, is its height greater than, less than, or equal to the height from which it was released?
Solution:
Assuming the ball starts spinning immediately upon encountering the non-slip surface, with no loss of energy, it will rise to the same height from which it was released. However, in a real system, some energy will be lost when the ball begins to spin. Therefore, the ball should reach a height slightly less than the height at which it was released.

Chapter 10 Rotational Kinematics and Energy Q.66P
Suppose the block in Example 10-6 has a mass of 2.1 kg and an initial upward speed of 0.33 m/s. Find the moment of inertia of the wheel if its radius is 8.0 cm and the block rises to a height of 7.4 cm before momentarily coming to rest.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy66ps

Chapter 10 Rotational Kinematics and Energy Q.67P
Through what height must the yo-yo in Active Example 10-3 fall for its linear speed to be 0.65 m/s?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy67ps

Chapter 10 Rotational Kinematics and Energy Q.68P
Suppose we change the race shown in Conceptual Checkpoint 10-4 to a race between three different disks. Let disk 1 have a mass M and a radius R, disk 2 have a mass M and a radius 2R, and disk 3 have a mass 2M and a radius R. Rank the three disks in the order in which they finish the race, indicate ties where appropriate.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy68ps

Chapter 10 Rotational Kinematics and Energy Q.69P
Calculate the speeds of (a) the disk and (b) the hoop at the bottom of the inclined plane in Conceptual Checkpoint 10-4 if the height of the incline is 0.82 m.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy69ps

Chapter 10 Rotational Kinematics and Energy Q.70P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy70p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.71P
In Conceptual Checkpoint 10-5, assume the ball is a solid sphere of radius 2.9 cm and mass 0.14 kg. If the ball is released from rest at a height of 0.78 m above the bottom of the track on the no-slip side, (a) what is its angular speed when it is on the
frictionless side of the track? (b) How high does the ball rise on the frictionless side?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy71ps

Chapter 10 Rotational Kinematics and Energy Q.72P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy72p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.73P
A 1.3-kg block is tied to a string that is wrapped around the rim of a pulley of radius 7.2 cm. The block is released from rest. (a) Assuming the pulley is a uniform disk with a mass of 0.31 kg, find the speed of the block after it has fallen through a height of 0.50 m. (b) If a small lead weight is attached near the rim of the pulley and this experiment is repeated, will the speed of the block increase, decrease, or stay the same? Explain.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy73ps

Chapter 10 Rotational Kinematics and Energy Q.74P
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy74p
Solution:

Chapter 10 Rotational Kinematics and Energy Q.75P
A 2.0-kg solid cylinder (radius = 0.10 m, length = 0.50 m) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.75 m high and 5.0 m long. When the cylinder rthees the bottom of the ramp, what are
(a) Its total kinetic energy, (b) its rotational kinetic energy, and (c) its translational kinetic energy?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy75ps

Chapter 10 Rotational Kinematics and Energy Q.76P
A2.5-kg solid sphere (radius = 0.10 m) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.75 m high and 5.6 m long. When the sphere rthees the bottom of the ramp, what are (a) its total kinetic energy, (b) its rotational kinetic energy, and (c) its translational kinetic energy?
GENERAL PROBLEMS
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy76ps

Chapter 10 Rotational Kinematics and Energy Q.77GP
When you stand on the observation deck of the Empire State Building in New York, is your linear speed due to the Earth’s rotation greater than, less than, or the same as when you were waiting for the elevators on the ground floor?
Solution:
Linear speed V=rw
When you stand on the top of the building, your distance (r) from the axis of rotation of Earth will be greater than it was on the ground. As a result, your linear speed at the top of the building is greater than when you were on the ground.

Chapter 10 Rotational Kinematics and Energy Q.78GP
One way to tell whether an egg is raw or hard boiled−without cracking it open−is to place it on a kitchen counter and give it a spin. If you do this to two eggs, one raw the other hard boiled, you will find that one spins considerably longer than the other. Is the raw egg the one that spins a long time, or the one that stops spinning in a short time?
Solution:
A hard-boiled egg spins for a longer time than a raw egg. A hard-boiled egg is rigid and spins with a uniform angular speed. However, the angular speed of a raw egg is not uniform because of its liquid inertia. The liquid inside tries to move away from the axis of rotation and increase its moment of inertia.

Chapter 10 Rotational Kinematics and Energy Q.79GP
When the Hoover Dam was completed and the reservoir behind it filled with water, did the moment of inertia of the Earth increase, decrease, or stay the same?
Solution:
The reservoir was filled by moving from a lower level to a higher level, moving this mass of water further from the axis of rotation. This slightly increases the moment of inertia of Earth.
l ∝r
As the distance from the axis of rotation (r) increases, I increases.

Chapter 10 Rotational Kinematics and Energy Q.80GP
In Quito, Ecuador, near the equator, you weigh about half a pound less than in Barrow, Alaska, near the pole. Find the rotational period of the Earth that would make you feel weightless at the equator. (With this rotational period, your centripetal acceleration would be equal to the acceleration due to gravity, g.)
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy80gps

Chapter 10 Rotational Kinematics and Energy Q.81GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy81gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.82GP
What linear speed must a 0.065-kg hula hoop have if its total kinetic energy is to be 0.12 J? Assume the hoop rolls an the ground without slipping.
Solution:
When the hoop rolls on the ground without slipping, the energy possessed is the sum of its rotational kinetic energy and translational kinetic energy. The translational kinetic energy is
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy82gps

Chapter 10 Rotational Kinematics and Energy Q.83GP
A pilot performing a horizontal turn will lose consciousness if she experiences a centripetal acceleration greater than 7.00 times the acceleration of gravity. What is the minimum radius turn she can make without losing consciousness if her plane is flying with a constant speed of 245 m/s?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy83gps

Chapter 10 Rotational Kinematics and Energy Q.84GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy84gp
Solution:

The center of the outer quarter moves in a circle that has double the radius of a quarter. As a result, the linear distance covered by the center of the outer part of the quarter is twice the circumference of a quarter. Therefore, if the outer quarter rolls without slipping, it must complete . two revolutions

Chapter 10 Rotational Kinematics and Energy Q.85GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy85gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.86GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy86gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.87GP
Referring to the previous problem, (a) estimate the linear speed of a point on the rim of the rotating disk. (b) By comparing the arc length between the two white lines to the distance covered by the BB, estimate the speed of the BB. (c) What radius must the disk have for the linear speed of a point on its rim to be the same as the speed of the BB? (d) Suppose a1.0-g lump of putty is stuck to the rim of the disk. What centripetal force is required to hold the putty in place?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy87gps

Chapter 10 Rotational Kinematics and Energy Q.88GP
A mathematically inclined friend e-mails you the following instructions: “Meet me in the cafeteria the first tune after 2:00 p.m. today that the hands of a clock point in the same direction.” (a) Is the desired meeting time before, after, or equal to 2:10 P.M.? Explain. (b) Is the desired meeting time before, after, or equal to 2:15 p.m.? Explain. (c) When should you meet your friend?
Solution:
Use the angle between the two vectors to know the first tune after 2.00 PM that the hands of a clock points in the same direction.
(a)
The hands of a clock are in same direction after 2.00 PM at 2.10 PM.
Hence, the desired time is equal to 2.10 PM.
(b)
The hands of a clock are in same direction after 2.00 PM at 2.10 PM.
Hence, the desired time is before 2.15 PM.
(c)
The hands of a clock are in same direction after 2.00 PM at 2.10 PM.
Hence, You meet your friend at . 2.10 PM.

Chapter 10 Rotational Kinematics and Energy Q.89GP
A diver runs horizontally off the end of a diving tower 3.0 m above the surface of the water with an initial speed of 2.6 m/s. During her fall she rotates with an average angular speed of 2.2 rad/s. (a) How many revolutions has she made when she hits the water? (b) How does your answer to part (a) depend on the diver’s initial speed? Explain.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy89gps

Chapter 10 Rotational Kinematics and Energy Q.90GP
A potter’s wheel of radius 6.8 cm rotates with a period of 0.52 s. What are (a) the linear speed and (b) the centripetal acceleration of a small lump of clay on the rim of the wheel? (c) How do your answers to parts (a) and (b) change if the period of rotation is doubled?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy90gps

Chapter 10 Rotational Kinematics and Energy Q.91GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy91gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.92GP
Pigeons arc bred to display a number of interesting characteristics. One breed of pigeon, the “roiler, ” is remarkable for the fact that it does a number of backward somersaults as it drops straight down toward the ground. Suppose a roller pigeon drops from rest and free falls downward for a distance of 14 m. If the pigeon somersaults at the rate of 12 rad/s, how many revolutions has it completed by the end of its fall?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy92gps

Chapter 10 Rotational Kinematics and Energy Q.93GP
As a marble with a diameter of 1.6 cm roils down an incline, its center moveswith a linear acceleration of 3.3 m/s2. (a) What is the angular acceleration of the marble? (b) What is the angular speed of the marble after it rolls for 1.5 s from rest?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy93gps

Chapter 10 Rotational Kinematics and Energy Q.94GP
A rubber ball with a radius of 3.2 cm rolls along the horizontal surface of a table with a constant linear speed v. When the ball rolls off the edge of the table, it falls 0.66 m to the floor below. If the ball completes 0.37 revolution during its fall, what was its lineal’ speed, v?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy94gps

Chapter 10 Rotational Kinematics and Energy Q.95GP
Acollege campus features a large fountain surrounded by a circular pool. Two students start at the northernmost point of the pool and walk slowly around it in opposite directions. (a) If the angularspeed of the student walking in the clockwise direction (as viewed from above) is 0.045 rad/s and the angular speed of the other student is 0.023 rad/s, how long does it take before they meet? (b) A t what angle, measured clockwise from due north, do the students meet? (c) If the difference in linear speed between the students is 0, 23 m/s, what is the radius of the fountain?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy95gps

Chapter 10 Rotational Kinematics and Energy Q.96GP
A yo-yo moves downward until it rthees the end of its string, where it “sleeps.” As it sleeps−that is, spins in place−its angular speed decreases from 35 rad/s to 25 rad/s. During this time it completes 120 revolutions. (a) How long did it take for the yo-yo to slow from 35 rad/s to 25 rad/s? (b) How long does it take for the yo-yo to slow from 25 rad/s to 15 rad/s? Assume a constant angular acceleration as the yo-yo sleeps.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy96gps

Chapter 10 Rotational Kinematics and Energy Q.97GP
(a) An automobile with tires of radius 32 cm accelerates from 0 to 45 mph in 9.1 s. Find the angular acceleration of the tires. (b) How does your answer to part (a) change if the radius of the tires is halved?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy97gps

Chapter 10 Rotational Kinematics and Energy Q.98GP
In Problems 75 and 76 we considered a cylinder and a solid sphere, respectively, rolling down a ramp. (a) Which object do yon expect to have the greater speed at the bottom of the ramp? (b) Verify your answer to part (a) by calculating the speed of the cylinder and of the sphere when they rthe the bottom of the ramp.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy98gps

Chapter 10 Rotational Kinematics and Energy Q.99GP
A centrifuge (Problem 22) with an angular speed of 6050 rpm produces a maximum centripetal acceleration equal to 6840 g (that is, 6840 times the acceleration of gravity). (a) What is the diameter of this centrifuge? (b) What force must the bottom of the sample holder exert on a 15.0-g sample under these conditions?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy99gps

Chapter 10 Rotational Kinematics and Energy Q.100GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy100gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.101GP
The rotor in a centrifuge has an initial angular speed of 430 rad/s. After 8.2 s of constant angular acceleration, its angular speed has increased to 550 rad/s. During this time, what were (a) the angular acceleration of the rotor and (b) the angle through which it turned?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy101gps

Chapter 10 Rotational Kinematics and Energy Q.102GP
A honey bee has two pairs of wings that can beat 250 times a second. Estimate (a) the maximum angular speed of the wings and (b) the maximum linear speed of a wing tip.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy102gps

Chapter 10 Rotational Kinematics and Energy Q.103GP
The Sun, with Earth in tow, orbits about the center of the Milky Way galaxy at a speed of 137 miles per second, completing one revolution every 240 million years. (a) Find the angular speed of the Sun relative to the center of the Milky Way. (b) Find the distance from the Sun to the center of the Milky Way.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy103gps

Chapter 10 Rotational Kinematics and Energy Q.104GP
A person walks into a room and switches on the ceiling fan. The fan accelerates with constant angular acceleration for 15 s until it rthees its operating angularspeed of 1.9 rotations/s− after that its speed remains constant as long as the switch is “on.” The person stays in the room for a short time; then, 5.5 minutes after turning the fan on, she switches it off again and leaves the room. The fan now decelerates with constant angular acceleration, taking 2.4 minutes to come to rest. What is the total number of revolutions made by the fan, from the time it was turned on until the time it stopped?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy104gps

Chapter 10 Rotational Kinematics and Energy Q.105GP
When astronauts return from prolonged space flights, they often suffer from bone loss, resulting in brittle bones that may take weeks for their bodies to rebuild. One solution may be to expose astronauts to periods of substantiai”g forces” in a centrifuge carried aboard their spaceship. To test this approach, NASA conducted a study in which four people spent 22 hours the in a compartment attached to the end of a 28-foot arm that rotated with an angular speed of 10.0 rpm. (a) What centripetal acceleration did these volunteersexperience? Express your answer in terms of g. (b) What was their linear speed?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy105gps

Chapter 10 Rotational Kinematics and Energy Q.106GP
The pulsar in the Crab nebula (Problem 9) was created by a supernova explosion that was observed on Earth in A.D. 1.054. Its current period of rotation (33.0 ms) is observed to be increasing by 1.26 × 10−5 seconds per year. (a) What is the angular acceleration of the pulsar in rad/s2? (b) Assuming the angular acceleration of the pulsar to be constant, how many years will it take for the pulsar to slow to a stop? (c) Under the same assumption, what was the period of the pulsar when it was created?
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy106gps

Chapter 10 Rotational Kinematics and Energy Q.107GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy107gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.108GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy108gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.109GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy109gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.110GP
A person rides on a 12-m-diameter Ferris wheel that rotates at the constant rate of 8.1 rpm. Calculate the magnitude and direction of the force that the seat exerts on a 65-kg person when he is (a) at the top of the wheel, (b) at the bottom of the wheel, and (c) halfway up the wheel.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy110gps

Chapter 10 Rotational Kinematics and Energy Q.111GP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy111gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.112PP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy112gp
Solution:
The centripetal acceleration is given as

From the graph, let us assume draw a line from 20rpm of x- axis such that all the curves cut these line. From that we can get the centripetal accelerations of the individual curve.
From the above equation greater the acceleration, greater will be the radius because radius is directly proportional to acceleration when angular speed is constant.
Curve 1 will have greater radius.
And the rank of the curves in the order of increasing radius is 4, 3, 2, 1

Chapter 10 Rotational Kinematics and Energy Q.113PP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy113gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.114PP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy114gp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.115PP
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy115pp
Solution:

Chapter 10 Rotational Kinematics and Energy Q.116IP
Suppose we race a disk and a hollow spherical, shell, like a basketball. The spherical shell has a mass M and a radius R; the disk has a mass 2M and a radius 2R. (a) Which object wins the race? If the two objects are released at rest, and the height of the ramp is h = 0.75 m, find the speed of (b) the disk and (c) the spherical shell when they rthe the bottom of the ramp.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy116ip

Chapter 10 Rotational Kinematics and Energy Q.117IP
Consider a race between the following three objects: object 1, a disk; object 2, a solid sphere; and object 3, a hollow spherical shell. All objects have the same mass and radius. (a) Rank the three objects in the order in which they finish the race. Indicate a tie where appropriate. (b) Rank the objects in order of increasing kinetic energy at the bottom of the ramp. Indicate a tie where appropriate.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy117ips

b) The total kinetic energy of all objects remains same according to conservation of energy

Chapter 10 Rotational Kinematics and Energy Q.118IP
(a) Suppose the radius of the axle the string wraps around is increased. Does the speed of the yo-yo after falling through a given height increase, decrease, or stay the same? (b) Find the speed of the yo-yo after falling from rest through a height h = 0.50 m if the radius of the axle is 0.0075 m. Everything else in Active Example 10-3 remains the same.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy118ips

Chapter 10 Rotational Kinematics and Energy Q.119IP
Suppose we use a new yo-yo that has the same mass as the original yo-yo and an axle of the same radius. The new yo-yo has a different mass distribution−most of its mass is concentrated near the rim. (a) Is the moment of inertia of the new yo-yo greater than, less than, or the same as that of the original yo-yo? (b) Find the moment of inertia of the new yo-yo if its speed after dropping from rest through a height h = 0.50 m is v = 0.64 m/s.
Solution:
Mastering Physics Solutions Chapter 10 Rotational Kinematics and Energy119ips

Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions

May 26, 2018May 25, 2018 by Prasanna

Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions

Mastering Physics Solutions

Chapter 9 Linear Momentum And Collisions Q.1CQ
If you drop your keys, their momentum increases as they fall. Why is the momentum of the keys not conserved? Does this mean that the momentum of the universe increases as the keys fail? Explain.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions1cqs
The momentum of the key is not conserved, because a net force acts on them. The momentum of the universe, however, is conserved because there are equal and opposite forces acting on Earth.

Chapter 9 Linear Momentum And Collisions Q.1P
Referring to Exercise 9-1, what speed must the baseball have if its momentum is to be equal in magnitude tothat of the car? Give your result in miles per hour.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions1ps

Chapter 9 Linear Momentum And Collisions Q.2CQ
By what factor does an object’s kinetic energy change if its speed is doubled? By what factor does its momentum change?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions2cqs

Chapter 9 Linear Momentum And Collisions Q.2P
Find the total momentum of the birds in Example 9-1 if the goose reverses direction.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions2ps

Chapter 9 Linear Momentum And Collisions Q.3CQ
A system of particles is known to have zero kinetic energy. What can you say about the momentum of the system?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions3cqs

Chapter 9 Linear Momentum And Collisions Q.3P
· · A26.2-kg dog is running northward at 2.70 m/s, while a 5.30-kg cat is running eastward at 3.04 m/s. Their 74.0-kg owner has the same momentum as the two pets taken together. Find the direction and magnitude of the owner’s velocity.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions3ps

Chapter 9 Linear Momentum And Collisions Q.4CQ
A system of particles is known to have zero momentum. Does it follow that the kinetic energy of the system is also zero? Explain.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions4cqps

Chapter 9 Linear Momentum And Collisions Q.4P
IP Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.35 kg and a speed of 1.2 m/s. Cart 2 has a mass of 0.61 kg. (a) What speed must cart 2 have if
the total momentum of the system is to be zero? (b) Since the momentum of the system is zero, does it follow that the kinetic energy of the system is also zero? (c) Verify your answer to part (b) by calculating the system’s kinetic energy
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions4ps

Chapter 9 Linear Momentum And Collisions Q.5CQ
On a calm day you connect an electric fan to a battery on your sailboat and generate a breeze. Can the wind produced by the fan be used to power the sailboat? Explain.
Solution:
Momentum is defined as the quantity of motion of the moving body, which is equal to the mass and its velocity. In other ward, momentum is the product of mass and velocity of the moving body. If the electric fan is connected to the battery on the sailboat, then electric fan generates the freeze that is winds. The winds generated by the fan which is faced the rear of the sailboat are used, and then winds pushed the sailboat and gives the momentum of the sailboat. So, sailboat moves in the same direction of the face of the sailboat. Therefore, the wind produced by the fan is used to power the sailboat. Hence, the wind is used to give the power to the sailboat.

Chapter 9 Linear Momentum And Collisions Q.5P
A 0.150-kg baseball is dropped from rest. If the magnitude of the baseball’s momentum is 0.780 kg · m/s just before it lands on the ground, from what height was it dropped?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions5ps

Chapter 9 Linear Momentum And Collisions Q.6CQ
In the previous question, can you use the wind generated by the fan to move a boat that has no sail? Explain whyor why not.
Solution:
Answer:
Yes, just point the fan to the rear of the boat.
When the boat is not sailing, then the total momentum of the system is zero. If the fan is placed to the rear end of the boat, then the fan pushes the water backward. So, in order to conserve the momentum, the water should push the boat forward. Hence, the resulting thrust will make the boat sail.

Chapter 9 Linear Momentum And Collisions Q.6P
IP A 285-g ball falls vertically downward, hitting the floor with a speed of 2.5 m/s and rebounding upward with a speed of 2.0 m/s. (a) Find the magnitude of the change in the ball’s momentum. (b) Find the change in the magnitude of the ball’s momentum. (c) Which of the two quantities calculated in parts (a) and (b) ismore directly related to the net force acting on the ball during its collision with the floor? Explain.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions6ps

Chapter 9 Linear Momentum And Collisions Q.7CQ
Crash statistics show that it is safer to be riding in a heavy car in an accident than in a light car. Explain in terms of physical principles.
Solution:
It is always safer to ride in a heavy car, because if a heavy car and a light one collide, the lighter car will move with greater acceleration than the heavier car after impact.
Force F = mass acceleration. When the heavy car collides with a light car, both the cars exert equal and opposite forces on each other. As the mass of the lighter car is less, it moves with greater acceleration, making it less safe for the rider.

Chapter 9 Linear Momentum And Collisions Q.7P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions7p
Solution:

Chapter 9 Linear Momentum And Collisions Q.8CQ
(a) As you approach a stoplight, youapply the brakes and bring your car to rest. What happened to your car’s initial momentum? (b) When the light turns green, you accelerate until you reach cruising speed. What force was responsible for increasing your car’s momentum?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions8cqs

Chapter 9 Linear Momentum And Collisions Q.8P
CE Your car rolls slowly in a parking lot and bangs into the metal base of a light pole. In terms of safety, is it better for your collision with the light pole to be elastic, inelastic, or is the safety risk the same for either case? Explain.
Solution:
It is better for you if the car has an inelastic collision because the impulse from the pole in an inelastic collision would be just enough to stop the car. In an elastic collision, however, the impulse from the car would be greater and would act on it for a shorter period, causing injury to the rider.

Chapter 9 Linear Momentum And Collisions Q.9CQ
An object at rest on a frictionless surface is struck by a second object. Is it possible for both objects to be at rest after the collision? Explain.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions9cqs

Chapter 9 Linear Momentum And Collisions Q.9P
CE Predict/Explain A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 100-g pebble, (a) Is the change of the boulder’s momentum in one second greater than, less than, or equal to the change of the pebble’s momentum in the same time period? (b) Choose the best explanation from among the following:
I. The large mass of the boulder gives it the greater momentum.
II. The force causes a much greater speed in the 100-g pebble, resulting in more momentum.
III. Equal force means equal change in momentum for a given time.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions9ps

Chapter 9 Linear Momentum And Collisions Q.10CQ
In the previous question, is it possible for one of the two objects to be at rest after the collision? Explain.
Solution:
Yes; for example, in a one-dimensional elastic collision of objects of equal mass, the objects “swap” speeds. Therefore, if one object is at rest before the collision, it is also possible for one object to be at rest after the collision.

Chapter 9 Linear Momentum And Collisions Q.10P
CE Predict/Explain Referring to the previous question, (a) is the change in the boulder’s speed in one second greater than, less than, or equal to the change in speed of the pebble in the same time period? (b) Choose the best explanation from among the following:
I. The large mass of the boulder results in a small acceleration.
II. The same force results in the same change in speed for a given time.
III. Once the boulder gets moving it is harder to stop than the pebble.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions10ps

Chapter 9 Linear Momentum And Collisions Q.11CQ
(a) Can two objects on a horizontal frictionless surface have a collision in which all the initial kinetic energy of the system is lost? Explain, and give a specific example if your answer is yes. (b) Can two such objects have a collision in which all the initial momentum of the system is lost? Explain, and give a specific example if your answer is yes.
Solution:
(a) Yes. If two objects with momentum of equal magnitude collide head-on in an inelastic collision, the two objects come to rest. The initial kinetic energy of the system is converted into internal energy and other forms of energy.
In an inelastic collision, the momentum is conserved, but the kinetic energy is not conserved. This is assuming that the external forces on the system sum to zero, or that the differences are negligible.
(b) No. The initial momentum is not lost unless an external force acts on the system.
No force is mentioned here, so we assume that there is no external force acting on the system, and the momentum of the system is conserved in all collisions.

Chapter 9 Linear Momentum And Collisions Q.11P
CE Predict/Explain A friend tosses a ball of mass m to you with a speed v. When you catch the ball, you feel a noticeable sting in your hand, due to the force required to stop the ball. (a) If you now catch a second ball, with a mass 2m and speed v/2,is the sting you feel greater than, less than, or equal to the sting you felt when you caught the first ball? The time required to stop the two balls is the same. (b) Choose the best explanation from among the following:
I. The second ball has less kinetic energy, since kinetic energy depends on v2, and hence it produces less sting.
II. The two balls have the same momentum, and hence they produce the same sting.
III. The second ball has more mass, and hence it produces the greater sting.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions11ps

Chapter 9 Linear Momentum And Collisions Q.12CQ
Two cars collide at an intersection. If the cars do not stick together, can we conclude that their collision was elastic? Explain.
Solution:
The collision between the two cars does not need to be elastic, even if the cars do not stick together.
This is because when the two cars collide, a certain amount of energy is dissipated in the form of sound, heat, and also in deforming the cars by forming dents. So the kinetic energy of the system is not conserved and the collision is not elastic.

Chapter 9 Linear Momentum And Collisions Q.12
CE Force A has a magnitude F and acts for the time △t, force B has a magnitude 2F and acts for the time △t/3, force C has a magnitude 5F and acts for the time △t/10,and force D has a magnitude l0F and acts for the time △t/100. Rank these forces in order of increasing impulse. Indicate ties where appropriate.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions12ps

Chapter 9 Linear Momentum And Collisions Q.13CQ
At the instant a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. Whichobject−the bullet or
the gun−has the greater kinetic energy? Explain. How does your answer apply to the observation that it is safe to hold a gun while it is fired, whereas the bullet is deadly?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions13cqs

Chapter 9 Linear Momentum And Collisions Q.13P
Find the magnitude of the impulse delivered to a soccer ball when a player kicks it with a force of 1250 N. Assume that the player’s foot is in contact with the ball for 5.95 ×10−3 s.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions13ps

Chapter 9 Linear Momentum And Collisions Q.14CQ
An hourglass is turned over, and the sand is allowed to pour from the upper half of the glass to the lower half. If the hourglass is resting on a scale, and the total mass of the hourglass and sand is M, describe the reading on the scale as the sand runs to the bottom.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions14cqs

Chapter 9 Linear Momentum And Collisions Q.14P
In a typical golf swing, the club is in contact with the ball for about 0.0010 a. If the 45-g ball acquires a speed of 67 m/s, estimate the magnitude of the force exerted by the club on the ball.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions14ps

Chapter 9 Linear Momentum And Collisions Q.15CQ
In the classic movie The Spirit of St. Louis, Jimmy Stewart portrays Charles Lindbergh on his history-making transatlantic flight. Lindbergh is concerned about the weight of his fuel-laden airplane. As he flies over Newfoundland he notices a fly on the dashboard. Speaking to the fly, he wonders aloud, “Does the plane weigh less if you fly inside it as it’s flying? Now that’s an interesting question.” What do you think?
Solution:
The weight of the plane is the same whether the fly is on the dashboard or inside the cockpit. This is because the fly exerts the same downward force (F=mg), regardless of whether it is on the dashboard or inside. This force acts downward on the plane. Thus, the effect is the same whether the fly is standing on the outside or the inside of the plane.

Chapter 9 Linear Momentum And Collisions Q.15P
A 0.50-kg croquet ball is initially at rest on the grass. When the ball is struck by a mallet, the average force exerted on it is 230 N. If the ball’s speed after being struck is 3.2 m/s, how long was the mallet in contact with the ball?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions15ps

Chapter 9 Linear Momentum And Collisions Q.16CQ
A tall, slender drinking glass with a thin base is initially empt. (a) Where is the center of mass of the glass? (b) Suppose the glass is now filled slowly with water until it is completely full. Describe the position and motion of the center of mass during the filling process.
Solution:
The center of mass of an object is the point where the entire mass of the object seems to be concentrated.
(a) If the base of the glass is very thin, the center of mass of the glass will be at its geometric center.
(b) When the glass is being filled with water, initially the center of mass for the system is below the center of mass for the glass. When the glass is completely filled with water, the center of mass will again be at the geometric center of the glass.

Chapter 9 Linear Momentum And Collisions Q.16P
(a) Can two objects on a horizontal frictionless surface have a collision in which all the initial kinetic energy of the system is lost? Explain, and give a specific example if your answer is yes.
(b) Can two such objects have a collision in which all the initial momentum of the system is lost? Explain, and give a specific example if your answer is yes
Solution:
(a) Yes If two objects with momentum of equal magnitude collide head-on in an linelastic collision the two objects come to restS The initial kinetic energy of the system is converted into internal energy and other forms of energy In an inelastic collision, the momentum is conserved, but the kinetic energy is not conserved This is assuming that the external forces on the system sum to zero, or that the differences are negligible
(b) No The initial momentum is not lost unless an external force acts on the system No force is mentioned here, so we assume that there is no external force acting on the system. and the momentum of the system is conserved in all collisions

Chapter 9 Linear Momentum And Collisions Q.17CQ
Lifting one foot into the air, you balance on the other foot. Wha t can you say about the location of yourcenter of mass?
Solution:
When you stand on one foot lifting the other one in air the entire body weight will be concentrated between ground and the foot which is in contact with the ground.
So your center of mass is somewhere directly above the area of contact between your foot and the ground.

Chapter 9 Linear Momentum And Collisions Q.17P
IP A 15.0-g marble is dropped from rest onto the floor 1.44 m below, (a) If the marble bounces straight upward to a height of 0.640 m, what are the magni tude and d irection of the impulse delivered to the marble by the floor? (b) If the marble had bounced to a greater height, would the impulse delivered to it have been greater or less than the impulse found in part (a)? Explain.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions17ps

Chapter 9 Linear Momentum And Collisions Q.18CQ
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions18cq
Solution:
As this jumper clears the bar, a significant portion of the body extends below the bar because of the extreme arching of his back. Just as the center of mass of a donut can lie outside the donut, the center of mass of the jumper can be outside his body. In extreme cases, the center of mass can even be below the bar at all times during the jump.

Chapter 9 Linear Momentum And Collisions Q.18P
To make a bounce pass, a player throws a 0.60-kg basketball toward the floor. The ball hits the floor with a speed of 5.4 m/s at an angle of 65° to the vertical. If the ball rebounds with the same speed and angle, what was the impulse delivered to it by the floor?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions18ps

Chapter 9 Linear Momentum And Collisions Q.19P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions19p
Solution:

Chapter 9 Linear Momentum And Collisions Q.20P
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions20ps

Chapter 9 Linear Momentum And Collisions Q.21P
In a situation similar to Example 9-3, suppose the speeds of the two canoes after they are pushed apart are 0.58 m/s for canoe 1 and 0.42 m/s for canoe 2. If the mass of canoe 1 is 320 kg, what is the mass of canoe 2?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions21ps

Chapter 9 Linear Momentum And Collisions Q.22P
Two ice skaters stand at rest in the center of an ice rink. When they push off against one another the 45-kg skater acquires a speed of 0.62 m/s. If the speed of the other skater is 0.89 m/s, what is this skater’s mass?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions22ps

Chapter 9 Linear Momentum And Collisions Q.23P
Suppose the bee in Active Example 9-2 has a mass of 0.175 g. If the bee walks with a speed of 1.41 cm/s relative to the still water, what is the speed of the 4.75-g stick relative to.the water?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions23ps

Chapter 9 Linear Momentum And Collisions Q.24P
An object initially at rest breaks into two pieces as the result of an explosion One piece has twice the kinetic energy of the other piece What is the ratio of the masses of the two pieces? Which piece has the larger mass?

An object initially at rest breaks into two pieces as the result of an explosion. One piece has twice the kinetic energy of the other piece. What is the ratio of the masses of the two pieces? Which piece has the larger mass?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions24ps

Chapter 9 Linear Momentum And Collisions Q.25P
A 92-kg astronaut and a 1200-kg satellite are at rest relative to the space shuttle. The astronaut pushes on the sa tellite, giving it a speed of 0.14 m/s directly away from the shuttle. Seven and a half seconds later the astronaut comes into contact with the shuttle. What was the initial distance from the shuttle to the astronaut?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions25ps

Chapter 9 Linear Momentum And Collisions Q.26P
IP An 85-kg lumberjack stands at one end of a 380-kg floating log, as shown in Figure 9-15. Both the log and the lumberjack are at rest initially. (a) If the lumberjack now trots toward the other end of the log with a speed of 2.7 m/s relative to the log, what is the lumberjack’s speed relative to the shore? Ignore friction between the log and the water. (b) If the mass of the log had been greater, would the lumberjack’s speed relative to the shore be greater than, less than, or the same as in part (a)? Explain, (c) Check your answer to part (b) by calculating the lumberjack’s speed relative to the shore for the case of a 450-kg log.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions26ps

Chapter 9 Linear Momentum And Collisions Q.27P
A plate drops onto a smooth floor and shatters into three nieces of equal mass. Two of the pieces go off with equal speeds v at right angles to one another. Find the speed and direction of the third piece.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions27ps

Chapter 9 Linear Momentum And Collisions Q.28P
A cart of mass m moves with a speed v on a frictionless air track and collides with an identical cart that is stationary. If the two carts stick together after the collision, what is the final kinetic energy of the system?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions28ps

Chapter 9 Linear Momentum And Collisions Q.29P
Suppose the car in Example 9-6 has an initial speed of 20.0 m/s and that the direction of the wreckage after the collision is 40.0° above the x axis. Find the initial speed of the minivan and the final speed of the wreckage.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions29ps

Chapter 9 Linear Momentum And Collisions Q.30P
Two 72.0-kg hockey players skating at 5.45 m/s collide and stick together. If the angle between their initial directions was 115°, what is their speed after the collision?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions30ps

Chapter 9 Linear Momentum And Collisions Q.31P
IP (a) Referring to Exercise 9-2, is the final kinetic energy of the car and truck together greater than, less than, or equal to the sum of the initial kinetic energies of the car and truck separately? Explain. (b) Verify your answer to part (a) by calculating the initial and final kinetic energies of the system.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions31ps

Chapter 9 Linear Momentum And Collisions Q.32P
IP A bullet with a mass of 4.0 g and a speed of 650 m/s is fired at a block of wood with a mass of 0.095 kg. The block rests on a frictionless surface, and is thin enough that the bullet passes completely through it. Immediately after the bullet exits the block, the speed of the block is 23 m/s. (a) What is the speed of the bullet when it exits the block? (b) Is the final kinetic energy of this system equal to, less than, or greater than the initial kinetic energy? Explain. (c) Verify your answer to part (b) by calculating the initial and final kinetic energies of the system.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions32ps

Chapter 9 Linear Momentum And Collisions Q.33P
IP A 0,420-kg block of wood hangs from the ceiling by a string, and a 0.0750-kg wad of putty is thrown straight upward, striking the bottom of the block with a speed of 5.74 m/s. The wad of putty sticks to the block. (a) Is the mechanical energy of this system conserved? (b) How high does the putty-block system rise above the original position of the block?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions33ps

Chapter 9 Linear Momentum And Collisions Q.34P
A 0.430-kg block is attached to a horizontal spring that is at its equilibrium length, and whose force constant is 20.0 N/m. The block rests on a fi-ictionless surface. A 0.0500-kg wad of putty is thrown horizontally at the block, hitting it with a speed of 2.30 m/s and sticking. How far does the putty-block system compress the spring?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions34ps

Chapter 9 Linear Momentum And Collisions Q.35P
Two objects moving with a speed v travel in opposite directions in a straight line. The objects stick together when they collide, and move with a speed of v/4after the collision, (a) What is the ratio of the final kinetic energy of the system to the initial kinetic energy? (b) What is the ratio of the mass of the more massive object to the mass of the less massive object?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions35ps

Chapter 9 Linear Momentum And Collisions Q.36P
The collision between a hammer and a nail can be considered to be approximately elastic, Calculate the kinetic energy acquired by a 12-g nail when it is struck by a 550-g hammer moving with an initial speed of 4.5 m/s.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions36ps

Chapter 9 Linear Momentum And Collisions Q.37P
A 732-kg car stopped at an intersection is rear-ended by a 1720-kg truck moving with a speed of 15.5 m/s. lf the car was in neutral and its brakes were off, so that the collision is approximately elastic, find the final speed of both vehicles after the collision.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions37ps

Chapter 9 Linear Momentum And Collisions Q.38P
CE Suppose you throw a rubber ball at an elephant that is charging directly at you (not a good idea). When the ball bounces back toward you, is its speed greater than, less than, or equal to the speed with which you threw it? Explain.
Solution:
The speed of the ball after bouncing off the elephant will be greate than the speed that it had brfore collision. As the elephant is a heavier object and the ball is a lighter object, when the ball bounces back of the elephant its speed will be nearly twice the speed with which it is thrown.

Chapter 9 Linear Momentum And Collisions Q.39P
IP A charging bull elephant with a mass of 5240 kg comes directly toward you with a speed of 4.55 m/s. You toss a 0.150-kg rubber ball at the elephant with a speed of 7.81 m/s. (a) When the ball bounces back toward you, what is its speed? (b) How do you account for the fact that the ball’s kinetic energy has increased?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions39ps

Chapter 9 Linear Momentum And Collisions Q.40P
Moderating a Neutron In a nuclear reactor, neutrons released by nuclear fission must be slowed down before they can trigger additional reactions in other nuclei. To see what sort of material is most effective in slowing (or moderating) a neutron, calculate the ratio of a neutron’s final kinetic energy to its initial kinetic energy, Kf/Ki, for a head-on elastic collision with each of the following stationary target particles. (Note: The mass of a neutron is m = 1.009 u, where the atomic mass unit, u, is defined as follows: 1 u = 1.66 × 10−27 kg.) (a) An electron (M = 5.49 × 10−4 u). (b) A proton (M = 1.007 u). (c) The nucleus of a lead atom (M = 207.2 u).
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions40ps

Chapter 9 Linear Momentum And Collisions Q.41P
In the apple-orange collision in Example 9-7, suppose the final velocity of the orange is 1.03 m/s in the negative y direction. What are the final speed and direction of the apple in this case?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions41ps

Chapter 9 Linear Momentum And Collisions Q.42P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions42p
Solution:

Chapter 9 Linear Momentum And Collisions Q.43P
In this problem we show that when one ball is pulled to the left in the photo on page 275, only a single ball recoils to the right−under ideal elastic-collision conditions. To begin, suppose that each ball has a mass m, · and that the ball coming in from the left strikes the other balls with a speed v0. Now, consider the hypothetical case of two balls recoiling to the right. Determinethe speed the two recoiling balls must have in order to satisfy (a) momentum conservation and (b) energy conservation. Since these speeds are not the same, it follows that momentum and energy cannot be conserved simultaneously with a recoil of two balls.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions43ps

Chapter 9 Linear Momentum And Collisions Q.44P
CE Predict/Explain A stalactite in a cave has drops of water falling from it to the cave floor below. The drops are equally
spaced in time and come in rapid succession, so that at any given moment there are many drops in midair. (a) Is the center of mass of the midair drops higher than, lower than, or equal to the halfway distance between the tip of the stalactite and the cave floor? (b) Choose the best explanation from among the following:
I. The drops bunch up as they near the floor of the cave.
II. The drops are equally spaced as they fall, since they are released at equal times.
III. Though equally spaced in time, the drops are closer together higher up.
Solution:
a) The center of mass is higher than the half way distance between the tip of the stalactite and the cave cover.
b) The reason is as the drops fall, their separations increases. With the drops more closely spaced on the upper half of their falls, the center of mass is shifted above the halfway mark.
So option III is correct.

Chapter 9 Linear Momentum And Collisions Q.45P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions45p
Solution:

Chapter 9 Linear Momentum And Collisions Q.46P
You are holding a shopping basket at the grocery store with two 0.56-kg cartons of cereal at the left end of the basket. The basket is 0.71 m long. Where should you place a 1.8-kg half gallon of milk, relative to the left end of the basket, so that the center of mass of your groceries is at the center of the basket?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions46ps

Chapter 9 Linear Momentum And Collisions Q.47P
Earth-Moon Center of Mass The Earth has a mass of 5.98 × 1024 kg, the Moon has a mass of 7.35 × 1022 kg, and their center-to-center distance is 3.85 × 108 m. How far from the center of the Earth is the Earth-Moon center of mass? Is the Earth-Moon center of mass above or below the surface of the Earth? By what distance? (As the Earth and Moon orbit one another, their centers orbit about their common center of mass.)
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions47ps

Chapter 9 Linear Momentum And Collisions Q.48P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions48p
Solution:

Chapter 9 Linear Momentum And Collisions Q.49P
CE A pencil standing upright on its eraser end falls over and lands on a table. As the pencil falls, its eraser does not slip. The following questions refer to the contact force exerted on the pencil by the tablethe positive x direction be in the direction the pencil with the positive y direction be vertically
upward. (a) During the pencil’s fall, is the x component of the contact force positive, negative, or zero? Explain. (b) Is the y component of the contact force greater than, less than, or equal to the weight of the pencil? Explain.
Solution:
Let the direction of the pencil in an upright position be in a positive y-direction.
Let the direction of the pencil, when it falls, be in the positive x-direction.
(a) As the direction of the fall of the pencil is in the positive x-direction, the x-component of the force is also in the same direction because when the pencil falls to the ground, its center of mass accelerates in the positive x-direction only. So the contact force has a positive horizontal component.
(b) We know that the acceleration of the center of mass of the pencil is non-zero, and is directed downwards. As the pencil is in contact with the table, the table exerts a force on the pencil, which is less than the weight of the pencil.

Chapter 9 Linear Momentum And Collisions Q.50P
A cardboard box is in the shape of a cube with each side of length L. If the top of the box is missing, where is the center of mass of the open box? Give your answer relative to the geometric center of the box.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions50ps

Chapter 9 Linear Momentum And Collisions Q.51P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions51p
Solution:

Chapter 9 Linear Momentum And Collisions Q.52P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions52p
Solution:

Chapter 9 Linear Momentum And Collisions Q.53P
· · IP Three uniform metersticks, each of mass m, are placed on the floor as follows: stick 1 lies along the y/axis from y = 0 to y = 1.0 m, stick 2 lies along the x axis from x = 0 to x = 1.0 m, stick 3 lies along the x axis from x = 1.0 m to x = 2.0 m. (a) Find the location of the center of mass of the metersticks. (b) How would the location of the center of mass be affected if the mass of the metersticks were doubled?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions53ps

Chapter 9 Linear Momentum And Collisions Q.54P
A 0.726-kg rope 2.00 meters long lies on a floor. You grasp one end of the rope and begin lifting it upward with a constant speed of 0.710 m/s. Eind the position and velocity of the rope’s center of mass from the time you begin lifting the rope to the time the last piece of rope lifts off the floor. Plot your results. (Assume the rope occupies negligible volume directly below the point where it is being lifted.)
Solution:

Chapter 9 Linear Momentum And Collisions Q.55P
Repeat the previous problem, this time lowering the rope onto a floor instead of lifting it.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions55ps

Chapter 9 Linear Momentum And Collisions Q.56P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions56p
Solution:

Chapter 9 Linear Momentum And Collisions Q.57P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions57p
Solution:

Chapter 9 Linear Momentum And Collisions Q.58P
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions58p
Solution:

Chapter 9 Linear Momentum And Collisions Q.59P
Rocks for a Rocket Engine A child sits in a wagon with a pile of 0.65-kg rocks. If she can throw each rock with a speed of 11 m/s relative to the ground, causing the wagon to move, how many rocks must she throw per minute to maintain a constant average speed against a 3.4-N force of friction?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions59ps

Chapter 9 Linear Momentum And Collisions Q.60P
A 57.8-kg person holding two 0.880-kg bricks stands on a 2.10-kg skateboard. Initially, the skateboard and the person are at rest. The person now throws the two bricks at the same time so that their speed relative to the person is 17.0 m/s, What is the recoil speed of the person and the skateboard relative to the ground, assuming the skateboard moves without friction?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions60ps

Chapter 9 Linear Momentum And Collisions Q.61P
In the previous problem, calculate the final speed of the person and the skateboard relative to the ground if the person throws the bricks one at a time. Assume that each brick is thrown with a speed of 17.0 m/s relative to the person.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions61ps

Chapter 9 Linear Momentum And Collisions Q.62P
A 0.540-kg bucket rests on a scale. Into this bucket you pour sand at the constant rate of 56.0 g/s. If the sand lands in the bucket with a speed of 3.20 m/s, (a) what is the reading of the scale when there is 0.750 kg of sand in the bucket? (b) What is the weight of the bucket and the 0.750 kg of sand?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions62ps

Chapter 9 Linear Momentum And Collisions Q.63P
IP Holding a long rope by its upper end, you lower it onto a scale. The rope has a mass of 0.13 kg per meter of length, and is lowered onto the scale at the constant rate of 1.4 m/s. (a) Calculate the thrust exerted by the rope as it lands on the scale. (b) At the instant when the amount of rope at rest on the scale has a weight of 2.5 N, does the scale read 2.5 N, more than 2.5 N, or less than 2.5 N? Explain. (c) Check y oui’ answer to part (b) by calculating the reading on the scale at this time.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions63ps

Chapter 9 Linear Momentum And Collisions Q.64GP
CE Object A has a mass m, object B has a mass 2m, and object C has a mass m/2. Rank these objects in order of increasing kinetic energy, given that they all have the same momentum. Indicate ties where appropriate.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions64ps

Chapter 9 Linear Momentum And Collisions Q.65GP
·CE Object A has a mass m,object B has a mass 4m, and object C has a mass m/4. Rank these objects in order of increasing momentum, given that they all have the same kinetic energy. Indicate ties where appropriate.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions65ps

Chapter 9 Linear Momentum And Collisions Q.66GP
CE Predict/Explain A block of wood is struck by a bullet. (a) Is the block more likely to be knocked over if the bullet is metal and embeds itself in the wood, or if the bullet is rubber and bounces off the wood? (b) Choose the best explanation from among the following;
I. The change in momentum when a bullet rebounds is larger than when it is brought to rest.
II. The metal bullet does more damage to the block.
III. Since the rubber bullet bounces off, it has little effect.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions66ps

Chapter 9 Linear Momentum And Collisions Q.67GP
CE A juggler performs a series of tricks with three bowling balls while standing on a bathroom scale. Is the average reading of the scale greater than, less than, or equal to the weight of the juggler plus the weight of the three balls? Explain.
Solution:
The scale supports the juggler and the three balls for an extended period of time. Therefore, the average reading of the scale is equal to the weight of the juggler, plus the weight of the three balls.

Chapter 9 Linear Momentum And Collisions Q.68GP
A72.5-kg tourist climbs the stairs to the top of the Washington Monument, which is 555 ft high, How far does the Earth move in the opposite direction as the tourist climbs?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions68ps

Chapter 9 Linear Momentum And Collisions Q.69GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions69p
Solution:

Chapter 9 Linear Momentum And Collisions Q.70GP
A car moving with an initial speed v collides with a second stationary car that is one-half as massive. After the collision the first car moves in the same direction as before with a speed v/3. (a) Find the final speed of the second car. (b) Is this collision clastic or inelastic?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions70gps

Chapter 9 Linear Momentum And Collisions Q.71GP
A 1.35-kg block of wood sits at the edge of a table, 0.782 m above the floor. A 0.0105-kg bullet moving horizontally with a speed of 715 m/s embeds itself within the block. What horizontal distance does the block cover before hitting the ground?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions71gps

Chapter 9 Linear Momentum And Collisions Q.72GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions72gp
Solution:

Chapter 9 Linear Momentum And Collisions Q.73GP
The Force of a Storm During a severe storm in Palm Beach, FL, on January 2, 1999, 31 inches of rain fell in a period of nine hours. Assuming that the raindrops hit the ground with a speed of 10 m/s, estimate the average upward force exerted by one square meter of ground to stop the falling raindrops during the storm. (Note: One cubic meter of water has a mass of 1000 kg.)
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions73gps

Chapter 9 Linear Momentum And Collisions Q.74GP
An apple that weighs 2.7 N falls vertically downward from rest for 1.4 s. (a) What is the change in the apple’s momentum per second? (b) What is the total change in its momentum during the 1.4-second fall?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions74gps

Chapter 9 Linear Momentum And Collisions Q.75GP
To balance a 35.5-kg automobile tire and wheel, a mechanic must place a 50.2-g lead weight 25.0 cm from the center of the wheel. When the wheel is balanced, its center of mass is exactly fat the center of the wheel. How far from the center of the wheel was its center of mass before the lead weight was added?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions75gps

Chapter 9 Linear Momentum And Collisions Q.76GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions76g
Solution:

Chapter 9 Linear Momentum And Collisions Q.77GP
IP A 63-kg canoeist stands in the middle of her 22-kg canoe. The canoe is 3.0 m long, and the end that is closest to land is 2.5 m from the shore. The canoeist now walks toward the shore until she contes to the end of the canoe. (a) When the canoeist stops at the end of her canoe, is her distance from the shore equal to, greater than, or less than 2.5 m? Explain. (b) Verify your answer to part (a) by calculating the distance from the canoeist to shore.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions77gps

Chapter 9 Linear Momentum And Collisions Q.78GP
In the previous problem, suppose the canoeist is 3.4 m from shore when she reaches the end of her canoe. What is the canoe’s mass?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions78gps

Chapter 9 Linear Momentum And Collisions Q.79GP
· · Referring to Problem 56, find the reading on the scale (a) before and (b) after the string breaks, assuming the ball falls through the liquid with an acceleration equal to 0.250g.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions79gps

Chapter 9 Linear Momentum And Collisions Q.80GP
A younghockey player stands at rest on the ice holding a 1.3-kg helmet. The player tosses the helmet with a speed of 6.5 m/s in a direction 11° above the horizontal, and recoils with a speed of 0.25 m/s. Find the mass of the hockey player.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions80gps

Chapter 9 Linear Momentum And Collisions Q.81GP
Suppose the air carts in Example 9-9 are both moving to the right initially. The cart to the left has a mass m and an initial speed v0; the cart to the right has an initial speed v0/2. If the center of mass of this system moves to the right with a speed 2v0/3,what is the mass of the cart on the right?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions81gps

Chapter 9 Linear Momentum And Collisions Q.82GP
A long, uniform rope with a mass of 0.135 kg per meter lies on the ground. You grab one end of the rope and lift it at the constant rate of 1.13 m/s. Calculate the upward force you must exert at the moment when the top end of the rope is 0.525 m above the ground.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions82gps

Chapter 9 Linear Momentum And Collisions Q.83GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions83gp
Solution:

Chapter 9 Linear Momentum And Collisions Q.84GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions84gp
Solution:

Chapter 9 Linear Momentum And Collisions Q.85GP
IP A fireworks rocket is launched vertically into the night sky with an initial speed of 44.2 m/s. The rocket coasts after being launched, then explodes and breaks into two pieces of equal mass 2.50 s later. (a) If each piece follows a trajectory that is initially at 45.0° to the vertical, what was their speed immediately a fter the explosion? (b) Wha t is the velocity of the rocket’s center of mass before and after the explosion? (c) What is the acceleration of the rocket’s center of mass before and after the explosion?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions85gps

Chapter 9 Linear Momentum And Collisions Q.86GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions86gp
Solution:

Chapter 9 Linear Momentum And Collisions Q.87GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions87gp
Solution:

Chapter 9 Linear Momentum And Collisions Q.88GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions88gp
Solution:

Chapter 9 Linear Momentum And Collisions Q.89GP
Two air carts of mass m1 = 0.84 kg and m2 = 0.42 kg are placed on a frictionless track. Cart 1 is at rest initially, arid has a spring bumper with a force constant of 690 N/m. Cart 2 has a flat metal surface for a bumper, and moves toward the bumper of the stationary cart with an initial speed v = 0.68 m/s. (a) What is the speed of the two carts at the moment when their speeds are equal? (b) How much energy is stored in the spring bumper when the carts have the same speed? (c) What is the final speed of the carts after the collision?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions89gps

Chapter 9 Linear Momentum And Collisions Q.90GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions90gp
Solution:

Chapter 9 Linear Momentum And Collisions Q.91GP
Two objects with masses m1 and m2 and initial velocities v1 and v2,i move along a straight line and collide elastically. Assuming that the objects move along the same straight line after the collision, show that their relative velocities are unchanged; that is, show that v1 − v2/ i = v2,f − v1,f(You can use the results given in Problem 88.)
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions91gps

Chapter 9 Linear Momentum And Collisions Q.92GP
Amplified Rebound Height Two small rubber balls are dropped from rest at a height h above a hard floor. When the balls are released, the lighter ball (with mass m)is directly above the heavier ball (with mass M). Assume the heavier ball reaches the floor first and bounces elastically; thus, when the balls collide, the ball of mass M is moving upwardwith a speed v and the ball of mass m is moving downward with essentially the same speed. In terms of h, find the height to which the ball of mass m rises after the collision. (Use the results given in Problem 88, and assume the balls collide at ground level.)
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions92gps

Chapter 9 Linear Momentum And Collisions Q.93GP
On a cold winter morning, a child sits on a sled resting on smooth ice. When the 9.75-kg sled is pulled with a horizontal force of 40.0 N, it begins to move with an acceleration of 2.32 m/s2. The 21.0-kg child accelerates too, hut with a smaller acceleration than that of the sled. Thus, the child moves forward relative to the ice, but slides backward relative to the sled. Find the acceleration of the child relative to the ice.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions93gps

Chapter 9 Linear Momentum And Collisions Q.94GP
An object of mass m undergoes an elastic collision with an identical object that is at rest. The collision is not head-on. Show that the angle between the velocities of the two objects after the collision is 90°.
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions94gps

Chapter 9 Linear Momentum And Collisions Q.95GP
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions95gp
Solution:

Chapter 9 Linear Momentum And Collisions Q.96GP
IP A uniform rope of length L and mass M rests on a table, (a) if you lift one end of the rope upward with a constant speed, v, show that the rope’s center of mass moves upward with constant acceleration. (b) Next, suppose you hold the rope suspended in air, with its lower end just touching the table. If you now lower the rope with a constant speed, v, onto the table, is the acceleration of the rope’s center of mass upward or downward? Explain your answer. (c) Find the magnitude and direction of the acceleration of the rope’s center of mass far the case described in part (b). Compare with part (a).
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions96gps

Chapter 9 Linear Momentum And Collisions Q.97PP
From the perspective of an observer on the planet, what is the spacecraft’s speed of approach?
A. v1+u
B. v1− u
C. u − vi
D. vf −u
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions97pps

Chapter 9 Linear Momentum And Collisions Q.98PP
From the perspective of an observer on the planet, what is the spacecraft’s speed of departure?
A. v1+u
B. vf− u
C. u − vf
D. vi − u
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions98pps

Chapter 9 Linear Momentum And Collisions Q.99PP
Set the speed of departure from Problem 98 equal to the speed of approach from Problem 97. Solving this relation for the final speed, vf, yields:
A. vf = v + u
B. vf = vi− u
C. vf = vi + 2u
D. vf = vi − 2u
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions99pps

Chapter 9 Linear Momentum And Collisions Q.100PP
Consider the special case in which vi = u. By what factor does the kinetic energy of the spacecraft increase as a result of the encounter?
A. 4
B. 8
C. 9
D. 16
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions100pps

Chapter 9 Linear Momentum And Collisions Q.101IP
Referring to Example 9-5 Suppose a bullet of mass m = 6.75 g is fired into a ballistic pendulum whose bob has a mass of M = 0.675 kg. (a) If the bob rises to a height of 0.128 m, what was the initial speed of the bullet? (b) What was the speed of the bullet-bob combination immediately after the collision takes place?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions101ips

Chapter 9 Linear Momentum And Collisions Q.102IP
Referring to Example 9-5 A bullet with a mass m = 8.10 g and an initial speed v0 = 320 m/s is fired into aballistic pendulum. Wha t mass must the bob have if the bullet-bob combination is to rise to a maximum height of 0.125 m after the collision?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions102ips

Chapter 9 Linear Momentum And Collisions Q.103IP
Referring to Example 9-9 Suppose that cart 1 has a mass of 3.00 kg and an initial speed of 0.250 m/s. Cart 2 has a mass of 1.00 kg and is at rest initially. (a) What is the final speed of the carts? (b) How much kinetic energy is lost as a result of the collision?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions103ips

Chapter 9 Linear Momentum And Collisions Q.104IP
Referring to Example 9-9 Suppose the two carts have equal masses and are both moving to the Light before the collision. The initial speed of cart 1 (on the left) is v0 and the initial speed of cart 2 (on the right) is v0/2.(a) What is the speed of the center of mass of this system? (b) What percentage of the initial kinetic energy is lost as a result of the collision? (c) Suppose the collision is elastic. What are the final speeds of the two carts in this case?
Solution:
Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions104ips

Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy

May 24, 2018May 24, 2018 by Prasanna

Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy

Mastering Physics Solutions

Chapter 8 Potential Energy And Conservation Of Energy Q.1CQ
Is it possible for the kinetic energy of an object to be negative? Is it possible for the gravitational potential energy of an object to be negative? Explain.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy1cqs

Chapter 8 Potential Energy And Conservation Of Energy Q.1P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy1p
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.2CQ
An avalanche occurs when a mass of snow slides down a steep mountain slope. Discuss the energy conversions responsible for water vapor rising to form clouds, falling as snow on a mountain, and then sliding down a slope as an avalanche.
Solution:
As water vapor rises, there is an increase in the gravitational potential energy of the system. Part of this potential energy is released as snow and falls onto the mountain. If an avalanche occurs, the snow on the mountain accelerates down the slope, converting more gravitational potential energy into kinetic energy.

Chapter 8 Potential Energy And Conservation Of Energy Q.2P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy2q
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.3CQ
If the stretch of a spring is doubled, the force it exerts is also doubled. By what factor does the spring’s potential energy increase?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy3cqs1

Chapter 8 Potential Energy And Conservation Of Energy Q.3P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy3p
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Chapter 8 Potential Energy And Conservation Of Energy Q.4CQ
When a mass is placed on top of a vertical spring, the spring compresses and the mass moves downward. Analyze this system in terms of its mechanical energy.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy4cqs

The initial mechanical energy of the system is the gravitational potential energy of the mass-Earth system. As the mass moves downward, the gravitational potential energy of the system decreases.
At the same time, the potential energy of the spring increases because it is compressed. Initially, the decrease in gravitational potential energy is greater than the increase in the spring’s potential energy, which means that the mass gains kinetic energy. Eventually, the increase in the spring’s energy equals the decrease in the gravitational energy, and the mass comes to rest.

Chapter 8 Potential Energy And Conservation Of Energy Q.4P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy4p
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Chapter 8 Potential Energy And Conservation Of Energy Q.5CQ
If a spring is stretched so far that it is permanently deformed, its force is no longer conservative. Why?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy5cqs

We know that the external force must be equal to the restoring force, and its direction is opposite to the direction of the restoring force. If the external force is greater than the restoring force, then the spring gets permanently deformed. In this situation, the work that was done to stretch the spring is not fully recovered. Some of the work is converted into the energy of the deformation. For this reason, the spring force is not conservative during deformation.

Chapter 8 Potential Energy And Conservation Of Energy Q.5P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy5p
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Chapter 8 Potential Energy And Conservation Of Energy Q.6CQ
An object is thrown upward to a person on a roof. At what point is the object’s kinetic energy at maximum? At what point is the potential energy of the system at maximum? At what locations do these energies have their minimum values?
Solution:
When the object is first thrown upward, its speed and its kinetic energy are at a maximum. Its potential energy is zero at that moment.
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy6cqs
(i) The potential energy of the system is at a maximum at the highest point of the object’s flight and is at a minimum at the starting point of its journey (when it has just been released).
(ii) The kinetic energy of the system is at maximum when the object has just been thrown up and is at a minimum when it reaches its highest point of flight.

Chapter 8 Potential Energy And Conservation Of Energy Q.6P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy6p
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.7CQ
It is a law of nature that the total energy of the universe is conserved. What do politicians mean, then, when they urge “energy conservation”?
Solution:
When the term “energy conservation” is used in everyday language, it doesn’t refer to the total amount of energy in the universe. Instead it refers to using energy wisely, especially when a particular source of energy like oil or natural gas is finite and non-renewable.

Chapter 8 Potential Energy And Conservation Of Energy Q.7P
Predict/Explain Ball 1 is thrown to the ground with an initial downward speed; ball 2 is dropped to the ground from rest. Assuming the balls have the same mass and are released from the same height, is the change in gravitational potential energy of ball 1 greater than, less than, or equal to the change in gravitational potential energy of ball 2? (b) Choose the best explanation from among the following:
I. Ball 1 has the greater total energy, and therefore more energy can go into gravitational potential energy.
II. The gravitational potential energy depends only on the mass of the ball and the drop height.
III. All of the initial energy of ball 2 is gravitational potential energy.
Solution:
(a) The change in gravitational potential energy of the ball 1 is equal to the change in gravitational potential energy of the ball 2.
(b) This is because the change in gravitational potential energy depends only on the mass of the ball and the height from which the ball is dropped. Therefore option II is the best explanation.

Chapter 8 Potential Energy And Conservation Of Energy Q.8CQ
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy8cq
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Chapter 8 Potential Energy And Conservation Of Energy Q.8P
A mass is attached to the bottom of a vertical spring. This causes the spring to stretch and the mass to move downward. (a) Does the potential energy of the spring increase, decrease, or stay the same during this process? Explain. (b) Does the gravitational potential energy of the Earth-mass system increase, decrease, or stay the same during this process? Explain.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.9CQ
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy9cq
Solution:
We have a photograph which shows an earthmover digging the earth and lifting it and loading it on the truck. In this situation, there are both conservative and non-conservative works involved.
Initially, the engine of the earthmover does positive, non-conservative work as it digs out and lifts a load of rocks. At the same time, gravity does negative, conservative work on the rocks as the gravitational potential energy of the system increases. As the rock is transported to the truck, the earthmover does positive, non-conservative work. When the rocks are released, gravity does positive, conservative work as the gravitational potential energy of the system is converted into kinetic energy. The kinetic energy of the rocks is converted into sound and heat when they are loaded into the truck.
As the truck is loaded, the spring is compressed. The potential energy is stored in the form of the spring’s potential energy, and the work done by the truck is conservative.

Chapter 8 Potential Energy And Conservation Of Energy Q.9P
As an Acapulco cliff diver drops to the water from a height of 46 m, his gravitational potential energy decreases by 25,000 J. What is the diver’s weight in newtons?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy9ps

Chapter 8 Potential Energy And Conservation Of Energy Q.10CQ
A toy frog consists of a suction cup and a spring. When the suction cup is pressed against a smooth surface, the frog is held down. When the suction cup lets go, the frog leaps into the air. Discuss the behavior of the frog in terms of energy conversions.
Solution:
The toy frog consists of a suction cup and a spring. When the suction cup is pressed, the energy of the toy is stored in the form of the spring as potential energy. When the suction cup lets go, then all its potential energy is converted into kinetic energy. As a result, the frog leaps into the air. The total energy of the system is conserved.

Chapter 8 Potential Energy And Conservation Of Energy Q.10P
Find the gravitational potential energy of an 88-kg person standing atop Mt. Everest at an altitude of 8848 m. Use sea level as the location for y = 0.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.11CQ
If the force on an object is zero, does that mean the potential energy of the system is zero? If the potential energy of a system is zero, is the force zero?
Solution:
No
Zero force implies a zero rate of change in the potential energy. However, the value of the potential energy can be anything at all. Similarly, if the potential energy is zero, it does not mean that the force is zero. Again, what matters is the rate of change of the potential energy.

Chapter 8 Potential Energy And Conservation Of Energy Q.11P
Jeopardy! Contestante on the game show Jeopardy! depress spring-loaded buttons to “buzz in” and provide the question corresponding to the revealed answer. The force constant on these buttons is about 130 N/m. Estimate the amount of energy it takes—at a minimum—to buzz in.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.12CQ
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy12cq
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Chapter 8 Potential Energy And Conservation Of Energy Q.12
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Chapter 8 Potential Energy And Conservation Of Energy Q.13CQ
When a ball is thrown upward, it spends the same amount of time on the way up as on the way down—as long as air resistance can be ignored. If air resistance is taken into account, is the time on the way down the same as, greater than, or less than the time on the way up? Explain.
Solution:
If the air resistance is taken into account, then the total mechanical energy of the system decreases. The distance covered by the ball is the same on the way down as it is on the way up, and so the amount of time will be determined by the average speed of the ball on the two portions of its trip. Note that air resistance does negative, non-conservative work continuously on the ball as it moves. Therefore, its total mechanical energy is less on the way down than it is on the way up, which means that its speed at any given elevation is less on the way down. It follows that more time is required for the downward portion of the trip.

Chapter 8 Potential Energy And Conservation Of Energy Q.13P
A vertical spring stores 0.962 J in spring potential energy when a 3.5-kg mass is suspended from it. (a) By what multiplicative factor does the spring potential energy change if the mass attached to the spring is doubled? (b) Verify your answer to part (a) by calculating the spring potential energy when a 7.0-kg mass is attached to the spring.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy13ps

Chapter 8 Potential Energy And Conservation Of Energy Q.14P
Pushing on the pump of a soap dispenser compresses a small spring. When the spring is compressed 0.50 cm, its potential energy is 0.0025 J. (a) What is the force constant of the spring? (b) What compression is required for the spring potential energy to equal 0.0084 J?
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.15P
A force of 4.1 N is required to stretch a certain spring by 1.4 cm. (a) How far must this spring be stretched for its potential energy to be 0.020 J? (b) How much stretch is required for the spring potential energy to be 0.080 J?
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.16P
The work required to stretch a certain spring from an elongation of 4.00 cm to an elongation of 5.00 cm is 30.5 J. (a) Is the work required to increase the elongation of the spring from 5.00 an to 6.00 cm greater than, less than, or equal to 30.5 J? Explain. (b) Verify your answer to part (a) by calculating the required work.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.17P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy17p
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Chapter 8 Potential Energy And Conservation Of Energy Q.18P
Predict/Explain You throw a ball upward and let it fall to the ground. Your friend drops an identical ball straight down to the ground from the same height. Is the change in kinetic energy of your ball greater than, less than, or equal to the change in kinetic energy of your friend’s ball? (b) Choose the best explanation from among the following:
I. Your friend’s ball converts all its initial energy into kinetic energy.
II. Your ball is in the air longer, which results in a greater change in kinetic energy.
III. The change in gravitational potential energy is the same for each ball, which means the change in kinetic energy must be the same also.
Solution:
(a) The Change in kinetic energy of your ball is equal to the change in kinetic energy of your friend’s ball.
(b) As both of you are at the same height, so when the balls come to the ground both balls lose same amount of potential energy. Therefore change in potential energy of the two balls is same. Then from conservation of energy the change in kinetic energy is also same.
So, option III is the best explanation.

Chapter 8 Potential Energy And Conservation Of Energy Q.19P
Suppose the situation described in Conceptual Checkpoint 8-2 is repeated on the fictional planet Epsilon, where the acceleration due to gravity is less than it is on the Earth. (a) Would the height of a hill on Epsilon that causes a reduction in speed from 4 m/s to 0 be greater than, less than, or equal to the height of the corresponding hill on Earth? Explain. (b) Consider the hill on Epsilon discussed in part (a). If the initial speed at the bottom of the hill is 5 m/s, will the final speed at the top of the hill be greater than, less than, or equal to 3 m/s? Explain.
Solution:
Solution:
(a) As we are considering on a planet Epsilon where the acceleration due to gravity is less than that on the earth and as the gravitational potential energy is mgh so larger height would be needed to gain the same level of gravitational potential energy. Thus, a higher hill would be needed.
(b) The initial speed at the bottom of the Epsilon is 5m/s which are the same on the earth. Since the values of the initial kinetic energy & final potential energies are the same on the Epsilon.
So therefore the final speed at the top of the hill on Epsilon is the same which is 3m/s

Chapter 8 Potential Energy And Conservation Of Energy Q.20P
Predict/Explain When a ball of mass m is dropped from. rest from a height h, its kinetic energy just before landing is K. Now, suppose a second ball of mass Am is dropped from rest from a height h/4. (a) Just before ball 2 lands, is its kinetic energy 4K, 2K, K, K/2, or K/4? (b) Choose the best explanation from among the following:
I. The two balls have the same initial energy.
II. The more massive ball will have the greater kinetic energy.
III. The reduced drop height results in a reduced kinetic energy.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy20ps

Chapter 8 Potential Energy And Conservation Of Energy Q.21P
Predict/Explain When a ball of mass m is dropped from rest from a height h, its speed just before landing is v. Now, suppose a second ball of mass 4m is dropped from rest from a height h/4. (a) Just before ball 2 lands, is its speed 4v, 2v, v, v/2, or v/4? (b) Choose the best explanation from among the following:
I. The factors of 4 cancel; therefore, the landing speed is the same.
II. The two balls land with the same kinetic energy; therefore, the ball of mass 4m has the speed v/2.
III. Reducing the height by a factor of 4 reduces the speed by a factor of 4.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.22P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy22p
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Chapter 8 Potential Energy And Conservation Of Energy Q.23P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy23p
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Chapter 8 Potential Energy And Conservation Of Energy Q.24P
At an amusement park, a swimmer uses a water slide to enter the main pool. If the swimmer starts at rest, slides without friction, and descends through a vertical height of 2.31 m, what is her speed at the bottom of the slide?
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.25P
In the previous problem, find the swimmer’s speed at the bottom of the slide if she starts with an initial speed of 0.840 m/s.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy25ps

Chapter 8 Potential Energy And Conservation Of Energy Q.26P
A player passes a 0.600-kg basket ball downcourt for a fast break. The ball leaves the player’s hands with a speed of 8.30 m/s and slows down to 7.10 m/s at its highest point. (a) Ignoring air resistance, how high above the release point is the ball when it is at its maximum height? (b) How would doubling the ball’s mass affect the result in part (a)? Explain.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.27P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy27p
Solution:
Here the all the three balls are at same height when they reached to the dashed line. And all the balls started from same height. Therefore the gain in potential energy of the three balls is same. Therefore the loss in kinetic energy of each ball is same. Also all the three balls have same initial speed. So all the three balls started with same speed and lost equal amount of kinetic energy. Therefore all the three balls have same speed at the dashes line. So, option (C) is correct.
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Chapter 8 Potential Energy And Conservation Of Energy Q.28P
In a tennis match, a player wins a point by hitting the ball sharply to the ground on the opponent’s side of the net. (a) If the ball bounces upward from the ground with a speed of 16 m/s, and is caught by a fan in the stands with a speed of 12 m/s, how high above the court is the fan? Ignore air resistance. (b) Explain why it is not necessary to know the mass of the tennis ball.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.29P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy29p
Solution:
Here the all the three balls are at same height when they reached to the dashed line. And all the balls started from same height. Therefore the gain in potential energy of the three balls is same. Therefore the loss in kinetic energy of each ball is same. Also all the three balls have same initial speed. So all the three balls started with same speed and lost equal amount of kinetic energy. Therefore all the three balls have same speed at the dashes line. So, option (C) is correct.

Chapter 8 Potential Energy And Conservation Of Energy Q.30P
A 2.9-kg block slides with a speed of 1.6 m/s on a frictionless horizontal surface until it encounters a spring. (a) If the block compresses the spring 4.8 cm before coming to rest, what is the force constant of the spring? (b) What initial speed should the block have to compress the spring by 1.2 cm?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy30ps

Chapter 8 Potential Energy And Conservation Of Energy Q.31P
A 0.26-kg rock is thrown vertically upward from the top of a cliff that is 32 m high. When it hits the ground at the base of the cliff, the rock has a speed of 29 m/s. Assuming that air resistance can be ignored, find (a) the initial speed of the rock and (b) the greatest height of the rock as measured from the base of the cliff.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy31ps

Chapter 8 Potential Energy And Conservation Of Energy Q.32P
A 1.40-kg block slides with a speed of 0.950 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 734 N/m. The block comes to rest after compressing the spring 4.15 cm. Find the spring potential energy, u, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of (a) 0 cm, (b) 1.00 cm, (c) 2.00 cm, (d) 3.00 cm, and (e) 4.00 cm.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.33P
A 5.76-kg rock is dropped and allowed to fall freely. Find the initial kinetic energy, the final kinetic energy, and the change in kinetic energy for (a) the first 2.00 m of fall and (b) the second 2.00 m of fall.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy33ps

If the mass of the bob increases, then the first part in the above equation decreases hence the speed of bob at point A increases. Therefore, the answer to part (b) increases as the mass increases.

Chapter 8 Potential Energy And Conservation Of Energy Q.34P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy34p
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Chapter 8 Potential Energy And Conservation Of Energy Q.35P
In the previous problem, (a) what is the bob’s kinetic energy at point B? (b) At some point the bob will come to rest momentarily. Without doing an additional calculation, determine the change in the system’s gravitational potential energy between point B and the point where the bob comes to rest. (c) Find the maximum angle the string makes with the vertical as the bob swings back and forth. Ignore air resistance.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.36P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy36p
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Chapter 8 Potential Energy And Conservation Of Energy Q.37P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy37p
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Chapter 8 Potential Energy And Conservation Of Energy Q.38P
You coast up a hill on your bicycle with decreasing speed. Your friend pedals up the hill with constant speed. (a) Ignoring friction, does the mechanical energy of the you-bike-Earth system increase, decrease, or stay the same? Explain. (b) Does the mechanical energy of the friend-bike-Earth system increase, decrease, or stay the same? Explain.
Solution:
(A) When a person coasts up a hill on his bicycle with decreasing speed, no non-conservative work is done on his bicycle. Therefore, his mechanical energy is conserved even though his speed decreases.
(B)
To maintain a constant speed, his friend will have to do positive non-conservative work while going uphill. Thus, his friend’s mechanical energy will increase.

Chapter 8 Potential Energy And Conservation Of Energy Q.39P
Predict/Explain On reentry, the space shuttle’s protective heat tiles become extremely hot. (a) Is the mechanical energy of the shuttle-Earth system when the shuttle lands greater than, less than, or the same as when it is in orbit? (b) Choose the best explanation from among the following:
I. Dropping out of orbit increases the mechanical energy of the shuttle.
II. Gravity is a conservative force.
III. A portion of the mechanical energy has been converted to heat energy.
Solution:
The mechanical energy E of a system is the sum of potential energy U and kinetic energy K.
Non conservative forces might decrease the mechanical energy by converting it to heat energy, or increase it by converting muscular work to kinetic or potential energy.
(a)
The space shuttle’s protective heat tiles become extremely hot, means that some amount of mechanical energy is converted to heat energy due to some non-conservative forces, and total mechanical energy of the system will decrease.
Thus, the mechanical energy of shuttle-Earth system when the shuttle lands is that of the mechanical energy when the shuttle is in orbit.
(b)
The space shuttle’s protective heat tiles become extremely hot, means that some amount of mechanical energy has been converted to heat energy.
Thus, the correct option is .

Chapter 8 Potential Energy And Conservation Of Energy Q.40P
Catching a wave, a 77-kg surfer starts with a speed of 1.3 m/s, drops through a height of 1.65 m, and ends with a speed of 8.2 m/s. How much nonconservative work was done on the surfer?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy40ps

Chapter 8 Potential Energy And Conservation Of Energy Q.41P
At a playground, a 19-kg child plays on a slide that drops through a height of 2.3 m. The child starts at rest at the top of the slide. On the way down, the slide does a nonconservative work of —361 J on the child. What is the child’s speed at the bottom of the slide?
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.42P
Starting at rest at the edge of a swimming pool, a 72.0-kg athlete swims along the surface of the water and reaches a speed of 1.20 m/s by doing the work Wnc1 = + 161 J. Find the nonconservative work, Wnc2, done by the water on the athlete.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.43P
A 17,000-kg airplane lands with a speed of 82 m/s on a stationary aircraft carrier deck that is 115 m long. Find the work done by nonconservative forces in stopping the plane.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.44P
The driver of a 1300-kg car moving at 17 m/s brakes quickly to 11 m/s when he spots a local garage sale. (a) Find the change in the car’s kinetic energy. (b) Explain where the “missing” kinetic energy has gone.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.45P
You ride your bicycle down a hill, maintaining a constant speed the entire time. (a) As you ride, does the gravitational potential energy of the you-bike-Earth system increase, decrease, or stay the same? Explain. (b) Does the kinetic energy of you and your bike increase, decrease, or stay the same? Explain. (c) Does the mechanical energy of the you-bike-Earth system increase, decrease, or stay the same? Explain.
Solution:
Solution:
(a) The gravitational potential energy of the earth-bike-rider system should decrease.
Since the position of the biker could eventually drop to ground level height, the potential energy of the system could go down to zero.
(b) Since the speed is constant throughout the entire time. The kinetic energy of you & your bike remains the same
(c) The mechanical energy of the system decrease. Since the total mechanical energy is equal to the sum of potential energy and kinetic energy. As the potential energy decreases & kinetic energy remains the same. So therefore the mechanical energy of the system decreases.

Chapter 8 Potential Energy And Conservation Of Energy Q.46P
Suppose the system in Example starts with m2 moving downward with a speed of 1.3 m/s. What speed do the masses have just before m2 lands?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy46ps

Chapter 8 Potential Energy And Conservation Of Energy Q.47P
A 42.0-kg seal at an amusement park slides from rest down a ramp into the pool below. The top of the ramp is 1.75 m higher than the surface of the water, and the ramp is inclined at an angle of 35.0° above the horizontal. If the seal reaches the water with a speed of 4.40 m/s, what are (a) the work done by kinetic friction and (b) the coefficient of kinetic friction between the seal and the ramp?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy47ps

Chapter 8 Potential Energy And Conservation Of Energy Q.48P
A 1.9-kg rock is released from rest at the surface of a pond 1.8 m deep. As the rock falls, a constant upward force of 4.6 N is exerted on it by water resistance. Calculate the nonconservative work, Wnc, done by water resistance on the rock, the gravitational potential energy of the system, u, the kinetic energy of the rock, K, and the total mechanical energy of the system, E, when the depth of the rock below the water’s surface is (a) 0 m, (b) 0.50 m, and (c) 1.0 m. Let y = 0 be at the bottom of the pond.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy48ps

Chapter 8 Potential Energy And Conservation Of Energy Q.49P
A 1250-kg car drives up a hill that is 16.2 m high. During the drive, two nonconservative forces do work on the car: (i) the force of friction, and (ii) the force generated by the car’s engine. The work done by friction is −3.11 × 105 J; the work done by the engine is + 6.44 × 105 J. Find the change in the car’s kinetic energy from the bottom of the hill to the top of the hill.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy49ps

Chapter 8 Potential Energy And Conservation Of Energy Q.50P
An 81.0-kg in-line skater does + 3420 J of nonconservative work by pushing against the ground with his skates. In addition, friction does −715 J of nonconservative work on the skater. The skater’s initial and final speeds are 2.50 m/s and 1.22 m/s, respectively. (a) Has the skater gone uphill, downhill, or remained at the same level? Explain. (b) Calculate the change in height of the skater.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy50ps

Chapter 8 Potential Energy And Conservation Of Energy Q.51P
In Example, suppose the two masses start from rest and are moving with a speed of 2.05 m/s just before m2 hits the floor. (a) If the coefficient of kinetic friction is µk = 0.350, what is the distance of travel, d, for the masses? (b) How much conservative work was done on this system? (c) How much non-conservative work was done on this system? (d) Verify the three work relations given in Equations 8-10.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.52P
A 15,800-kg truck is moving at 12.0 m/s when it starts down a 6.00° incline in the Canadian Rockies. At the start of the descent the driver notices that the altitude is 1630 m. When she reaches an altitude of 1440 m, her speed is 29.0 m/s. Find the change in (a) the gravitational potential energy of the system and (b) the truck’s kinetic energy. (c) Is the total mechanical energy of the system conserved? Explain.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy52ps

Chapter 8 Potential Energy And Conservation Of Energy Q.53P
A 1.80-kg block slides on a rough horizontal surface. The block hits a spring with a speed of 2.00 m/s and compresses it a distance of 11.0 cm before coming to rest. If the coefficient of kinetic friction between the block and the surface is µk = 0.560, what is the force constant of the spring?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy53ps

Chapter 8 Potential Energy And Conservation Of Energy Q.54P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy54p
Solution:

The above figure shows that, the object is at rest at initial point A. As the object moves from A to B, some of its potential energy is converted into kinetic energy, and the speed of the object increases at B. So the kinetic energy of the object increases when potential energy decreases.
Now the object moves from point B to point C. In this process, some of its kinetic energy is again converted into potential energy, thus, the speed of the object decreases as it moves from B to C. The object’s speed again increases as it moves from point C to point D, so its potential energy decreases while its kinetic energy increases.
Finally from point D to point E, the kinetic energy of the object decreases as curve rises. Thus, the speed of the object decreases. Therefore, at point E, the speed of the object momentarily becomes zero.

Chapter 8 Potential Energy And Conservation Of Energy Q.55P
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Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.56P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy56p
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Chapter 8 Potential Energy And Conservation Of Energy Q.57P
A 23-kg child swings back and forth on a swing suspended by 2.5-m-long ropes. Plot the gravitational potential energy of this system as a function of the angle the ropes make with the vertical, assuming the potential energy is zero when the ropes are vertical. Consider angles up to 90° on either side of the vertical.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.58P
Find the turning-point angles in the previous problem if the child has a speed of 0.89 m/s when the ropes are vertical. Indicate the turning points on a plot of the system’s potential energy.
Solution:
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Chapter 8 Potential Energy And Conservation Of Energy Q.59P
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy59p
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Chapter 8 Potential Energy And Conservation Of Energy Q.60P
A block of mass m = 0.95 kg is connected to a spring of force constant k = 775 N/m on a smooth, horizontal surface. (a) Plot the potential energy of the spring from x = −5.00 cm to x = 5.00 cm. (b) Determine the turning points of the block if its speed at x = 0 is 1.3 m/s.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy60ps

Chapter 8 Potential Energy And Conservation Of Energy Q.61P
A ball of mass m = 0.75 kg is thrown straight upward with an initial speed of 8.9 m/s. (a) Plot the gravitational potential energy of the block from its launch height, y = 0, to the height y = 5.0 m. Let u = 0 correspond to y = 0. (b) Determine the turning point (maximum height) of this mass.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy61ps

Chapter 8 Potential Energy And Conservation Of Energy Q.62P
Two blocks, the of mass m, are connected on a frictionless horizontal table by a spring of force constant k and equilibrium length L. Find the maximum and minimum separation between the two blocks in terms of their maximum speed, vmax,relative to the table. (The two blocks always move in opposite directions as they oscillate back and forth about a fixed position.)
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy62ps

Chapter 8 Potential Energy And Conservation Of Energy Q.63GP
You and a friend both solve a problem involving a skier going down a slope. When comparing solutions, you notice that your choice for the y = 0 level is different than the y = 0 level chosen by your friend. Will your answers agree or disagree on the following quantities: (a) the skier’s potential energy; (b) the skier’s change in potential energy; (c) the skier’s kinetic energy?
Solution:
Answer:
Your answers will disagree on (a), but agree on (b) and (c)
The gravitational potential energy depends upon the reference level but not the change in potential energy. The work done by gravity must be the same in the two solutions so change in potential energy and change in kinetic energy should be same.

Chapter 8 Potential Energy And Conservation Of Energy Q.64GP
A particle moves under the influence of a conservative force. At point A the particle has a kinetic energy of 12 J; at point 13 the particle is momentarily at rest, and the potential energy of the system is 25 J; at point C the potential energy of the system is 5 J. (a) What is the potential energy of the system when the particle is at point A? (b) What is the kinetic energy of the particle at point C?
Solution:
(a) In the given data the particle is at rest at point B having potential energy 25J. Therefore the total energy of the particle is 25J.
Now at point A the particle has kinetic energy of 12J.
Therefore the potential energy of the system at point A is 25J-12J=13J
(b) Now at point C the particle has potential energy of 5J.
Therefore the kinetic energy of the system at point C is 25J-5J=20J

Chapter 8 Potential Energy And Conservation Of Energy Q.65GP
A leaf falls to the ground with constant speed. Is ui + Ki for this system greater than, less than, or the same as uf + Kf for this system? Explain.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy65ps

Chapter 8 Potential Energy And Conservation Of Energy Q.66GP
Consider the two-block system shown in Example. (a) As block 2 descends through the distance d, does its mechanical energy increase, decrease, or stay the same? Explain. (b) Is the nonconservative work done on block 2 by the tension in the rope positive, negative, or zero? Explain.
Solution:
Solution:
(a) Since there is no conservative work with this system (the friction from mass 1) the mechanical energy of the system will change. Specifically, the mechanical energy of the system will decrease due to energy being converted into heat by the friction forces.
(b) The tension in the rope deals with the weight of the block that’s dropping down. The non conservative force comes from the friction of the block on the table. The tension in the rope simply deals with mass and gravitational acceleration thus, the tension in the rope is involved in potential/kinetic energy relations, and the amount of non conservative work it does is zero.

Chapter 8 Potential Energy And Conservation Of Energy Q.67GP
Taking a leap of faith, a bungee jumper steps off a plat-form and falls until the cord brings her to rest. Suppose you analyze this system by choosing y = 0 at the platform level, and your friend chooses y = 0 at ground level. (a) Is the jumper’s initial potential energy in your calculation greater than, less than, or equal to the same quantity in your friend’s calculation? Explain. (b) Is the change in the jumper’s potential energy in your calculation greater than, less than, or equal to the same quantity in your friend’s calculation? Explain.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy67gps

Chapter 8 Potential Energy And Conservation Of Energy Q.68GP
A sled slides without friction down a small, ice-covered hill. If the sled starts from rest at the top of the hill, its speed at the bottom is 7.50 m/s. (a) On a second run, the sled starts with a speed of 1.50 m/s at the top. When it reaches the bottom of the hill, is its speed 9.00 m/s, more than 9.00 m/s, or less than 9.00 m/s? Explain. (b) Find the speed of the sled at the bottom of the hill after the second run.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy68gps

Chapter 8 Potential Energy And Conservation Of Energy Q.69GP
In the previous problem, what is the height of the hill?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy69gps

Chapter 8 Potential Energy And Conservation Of Energy Q.70GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy70gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.71GP
Running Shoes The soles of a popular make of running shoe have a force constant of 2.0 × 105 N/m. Treat the soles as ideal springs for the following questions. (a) If a 62-kg person stands in a pair of these shoes, with her weight distributed equally on both feet, how much does she compress the soles? (b) How much energy is stored in the soles of her shoes when she’s standing?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy71gps

Chapter 8 Potential Energy And Conservation Of Energy Q.72GP
Nasal Strips The force required to flex a nasal strip and apply it to the nose is 0.25 N; the energy stored in the strip when flexed is 0.0022 J. Assume the strip to be an ideal spring for the following calculations. Find (a) the distance through which the strip is flexed and (b) the force constant of the strip.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy72gps

Chapter 8 Potential Energy And Conservation Of Energy Q.73GP
A pendulum bob with a mass of 0.13 kg is attached to a string with a length of 0.95 m. We choose the potential energy to be zero when the string makes an angle of 90° with the vertical. (a) Find the potential energy of this system when the string makes an angle of 45° with the vertical. (b) Is the magnitude of the change in potential energy from an angle of 90° to 45° greater than, less than, or the same as the magnitude of the change from 45° to 0°? Explain. (c) Calculate the potential energy of the system when the string is vertical.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy73gps

Chapter 8 Potential Energy And Conservation Of Energy Q.74GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy74gps
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.75GP
An 1865-kg airplane starts at rest on an airport runway at sea level. (a) What is the change in mechanical energy of the airplane if it climbs to a cruising altitude of 2420 m and maintains a constant speed of 96.5 m/s? (b) What cruising speed would the plane need at this altitude if its increase in kinetic energy is to be equal to its increase in potential energy?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy75gps

Chapter 8 Potential Energy And Conservation Of Energy Q.76GP
At the local playground a child on a swing has a speed of 2.02 m/s when the swing is at its lowest-point. (a) To what maximum vertical height does the child rise, assuming he sits still and “coasts”? Ignore air resistance. (b) How do your results change if the initial speed of the child is halved?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy76gps

Chapter 8 Potential Energy And Conservation Of Energy Q.77GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy77gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.78GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy78gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.79GP
A person is to be released from rest on a swing pulled away from the vertical by an angle of 20.0°. The two frayed ropes of the swing are 2.75 m long, and will break if the tension in either of them exceeds 355 N. (a) What is the maximum weight the person can have and not break the ropes? (b) If the person is released at an angle greater than 20.0°, does the maximum weight increase, decrease, or stay the same? Explain.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy79gps

Chapter 8 Potential Energy And Conservation Of Energy Q.80GP
A car is coasting without friction toward a hill of height h and radius of curvature r. (a) What initial speed, v0, will result in the car’s wheels just losing contact with the roadway as the car crests the hill? (b) What happens if the initial speed of the car is greater than the value found in part (a)?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy80gps

Chapter 8 Potential Energy And Conservation Of Energy Q.81GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy81gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.82GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy82gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.83GP
An 8.70-kg block slides with an initial speed of 1.56 m/s up a ramp inclined at an angle of 28.4° with the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.62. Use energy conservation to find the distance the block slides before coming to rest.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy83gps

Chapter 8 Potential Energy And Conservation Of Energy Q.84GP
Repeat the previous problem for the case of an 8.70-kg block sliding down the ramp, with an initial speed of 1.56 m/s.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy84gps

Chapter 8 Potential Energy And Conservation Of Energy Q.85GP
Jeff of the Jungle swings on a 7.6-m vine that initially makes an angle of 37° with the vertical. If Jeff starts at restand has a mass of 78 kg, what is the tension in the vine at the lowest point of the swing?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy85gps

Chapter 8 Potential Energy And Conservation Of Energy Q.86GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy86gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.87GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy87gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.88GP
Compressing the Ground A running track at Harvard University uses a surface with a force constant of 2.5 × 105 N/m This surface is compressed slightly every time a runner’s foot lands on it. The force exerted by the foot, according to the Saucony shoe company, has a magnitude of 2700 N for a typical runner. Treating the track’s surface as an ideal spring, find (a) the amount of compression caused by a foot hitting the track and (b) the energy stored briefly in the track every time a foot lands.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy88gps

Chapter 8 Potential Energy And Conservation Of Energy Q.89GP
A Flea’s Jump The resilin in the upper leg (coxa) of a flea has a force constant of about 26 N/m, and when the Flea cocks its jumping legs, the resilin in the leg is stretched by approximately 0.10 mm. Given that the flea has a mass of 0.50 mg, and that two legs are used in a jump, estimate the maximum height a flea can attain by using the energy stored in the resilin. (Assume the resilin to be an ideal spring.)
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy89gps

Chapter 8 Potential Energy And Conservation Of Energy Q.90GP
A trapeze artist of mass m swings on a rope of length L. Initially, the trapeze artist is at rest and the rope makes an angle θ with the vertical. (a) Find the tension in the rope when it is vertical. (b) Explain why your result for part (a) depends on L in the way it does.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy90gps

Chapter 8 Potential Energy And Conservation Of Energy Q.91GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy91gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.92GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy92gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.93GP
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Chapter 8 Potential Energy And Conservation Of Energy Q.94GP
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Chapter 8 Potential Energy And Conservation Of Energy Q.95GP
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Chapter 8 Potential Energy And Conservation Of Energy Q.96GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy96gp
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Chapter 8 Potential Energy And Conservation Of Energy Q.97GP
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Chapter 8 Potential Energy And Conservation Of Energy Q.98GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy98gp
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Chapter 8 Potential Energy And Conservation Of Energy Q.99GP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy99gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.100PP
The Flight of the Dragonflies
Of all the animals you’re likely to see on a summer’s day, the most ancient is the dragonfly. In fact, the fossil record for dragonflies extends back over 250 million years, more than twice as long as for birds. Ancient dragonflies could be as large as a hawk, and were surely buzzing around the heads of both T. Rex and Triceratops.
Dragonflies belong to the order Odonata (“toothed jaws”) and the suborder Anisoptera (“different wings”), a reference to the fact that their hindwings are wider front-to-back than their forewings. (Damselflies, in contrast, have forewings and hind-wings that are the same.) Although ancient in their lineage, dragonflies are the fastest flying and most acrobatic of all insects; some of their maneuvers subject them to accelerations as great as 20g.
The properties of dragonfly wings, and how they account for such speed and mobility, have been of great interest to biologists. Figure shows an experimental setup designed to measure the force constant of Plexiglas models of wings, which are used in wind tunnel tests. A downward force is applied to the model wing at the tip (1 for hindwing, 2 for forewing) or at two-thirds the distance to the tip (3 for hindwing, 4 for forewing). As the force is varied in magnitude, the resulting deflection of the wing is measured. The results are shown in Figure. Notice that significant differences are seen between the hindwings and forewings, as one might expect from their different shapes.
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy100gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.101PP
The Flight of the Dragonflies
Of all the animals you’re likely to see on a summer’s day, the most ancient is the dragonfly. In fact, the fossil record for dragonflies extends back over 250 million years, more than twice as long as for birds. Ancient dragonflies could be as large as a hawk, and were surely buzzing around the heads of both T. Rex and Triceratops.
Dragonflies belong to the order Odonata (“toothed jaws”) and the suborder Anisoptera (“different wings”), a reference to the fact that their hindwings are wider front-to-back than their forewings. (Damselflies, in contrast, have forewings and hind-wings that are the same.) Although ancient in their lineage, dragonflies are the fastest flying and most acrobatic of all insects; some of their maneuvers subject them to accelerations as great as 20g.
The properties of dragonfly wings, and how they account for such speed and mobility, have been of great interest to biologists. Figure shows an experimental setup designed to measure the force constant of Plexiglas models of wings, which are used in wind tunnel tests. A downward force is applied to the model wing at the tip (1 for hindwing, 2 for forewing) or at two-thirds the distance to the tip (3 for hindwing, 4 for forewing). As the force is varied in magnitude, the resulting deflection of the wing is measured. The results are shown in Figure. Notice that significant differences are seen between the hindwings and forewings, as one might expect from their different shapes.
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy101gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.102PP
The Flight of the Dragonflies
Of all the animals you’re likely to see on a summer’s day, the most ancient is the dragonfly. In fact, the fossil record for dragonflies extends back over 250 million years, more than twice as long as for birds. Ancient dragonflies could be as large as a hawk, and were surely buzzing around the heads of both T. Rex and Triceratops.
Dragonflies belong to the order Odonata (“toothed jaws”) and the suborder Anisoptera (“different wings”), a reference to the fact that their hindwings are wider front-to-back than their forewings. (Damselflies, in contrast, have forewings and hind-wings that are the same.) Although ancient in their lineage, dragonflies are the fastest flying and most acrobatic of all insects; some of their maneuvers subject them to accelerations as great as 20g.
The properties of dragonfly wings, and how they account for such speed and mobility, have been of great interest to biologists. Figure shows an experimental setup designed to measure the force constant of Plexiglas models of wings, which are used in wind tunnel tests. A downward force is applied to the model wing at the tip (1 for hindwing, 2 for forewing) or at two-thirds the distance to the tip (3 for hindwing, 4 for forewing). As the force is varied in magnitude, the resulting deflection of the wing is measured. The results are shown in Figure. Notice that significant differences are seen between the hindwings and forewings, as one might expect from their different shapes.
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy102gp

Solution:
From the graph it is clear that by the application of same force the deflection of wing is more for hindwing than the forewing.
Therefore force constant of forewing is greater than the force constant of hindwing.
So forewing is stiffer than the hindwing.
Therefore option B. is correct.

Chapter 8 Potential Energy And Conservation Of Energy Q.103PP
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy103gp
Solution:

Chapter 8 Potential Energy And Conservation Of Energy Q.104IP
Referring to Example Consider a spring with a force constant of 955 N/m. (a) Suppose the mass of the block is 1.70 kg, but its initial speed can be varied. What initial speed is required to give a maximum spring compression of 4.00 cm? (b) Suppose the initial speed of the block is 1.09 m/s, but its mass can be varied. What mass is required to give a maximum spring compression of 4.00 cm?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy104gps

Chapter 8 Potential Energy And Conservation Of Energy Q.105IP
Referring to Example Suppose the block is released from rest with the spring compressed 5.00 cm. The mass of the block is 1.70 kg and the force constant of the spring is 955 N/m. (a) What is the speed of the block when the spring expands to a compression of only 2.50 cm? (b) What is the speed of the block after it leaves the spring?
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy105gps

Chapter 8 Potential Energy And Conservation Of Energy Q.106IP
Referring to Example Suppose we would like the landing speed of block 2 to be increased to 1.50 m/s. (a) Should the coefficient of kinetic friction between block 1 and the table-top be increased or decreased? (b) Find the required coefficient of kinetic friction for a landing speed of 1.50 m/s. Note that m1 = 2.40 kg, m2 = 1.80 kg, and d = 0.500 m.
Solution:
Mastering Physics Solutions Chapter 8 Potential Energy And Conservation Of Energy106gps

Mastering Physics Solutions Chapter 7 Work And Kinetic Energy

May 23, 2018May 23, 2018 by Prasanna

Mastering Physics Solutions Chapter 7 Work And Kinetic Energy

Mastering Physics Solutions

Chapter 7 Work And Kinetic Energy Q.1CQ
Is it possible to do work on an object that remains at rest?
Solution:
No.
We know that work is said to be done only when a body moves a certain distance in the direction of an applied force. In other words, if no external force is applied or the body fails to move in the direction of an applied force, the work done is said to be zero.
Consider a block of mass m (kg) moving a distance d (m) by application of force F (N) in the direction of the motion. Then, work done
W = F·d = force distance
If d = 0 [i.e., the body is at rest]
W = F 0
= 0
Therefore, it is not possible to do work on an object that is at rest.

Chapter 7 Work And Kinetic Energy Q.1P
The International Space Station orbits the Earth in an approximately circular orbit at a height of h = 375 km above the Earth’s surface. In one complete orbit, is the work done by the Earth on the space station positive, negative, or zero? Explain.
Solution:
The work done by Earth on the space station is zero. This is because during the movement of the satellite, the force acting on it is always perpendicular to the direction of motion. If the force does not have non-zero components along the direction of motion, the work done is zero.

Chapter 7 Work And Kinetic Energy Q.2CQ
A friend makes the statement, “Only the total force acting on an object can do work.” Is this statement true or false? If it is true, state why; if it is false, give a counterexample.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy2cqs

Chapter 7 Work And Kinetic Energy Q.2P
A pendulum bob swings from point I to point II along the circular arc indicated in Figure. (a) Is the work done on the bob by gravity positive, negative, or zero? Explain. (b) Is the work done on the bob by the string positive, negative, or zero? Explain.
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy2p
Solution:
(a) When the pendulum bob swings from point I to point II along the circular arc, its displacement is downward. This is in the direction of force of gravity. Therefore the work done by the gravity is positive when the pendulum bob swings from point I to pint II along the circular arc.
(b) When the pendulum bob swings from point I to point II along the circular arc, the tension in the string is always perpendicular to its direction of motion. Therefore the work done by the string is zero when the pendulum bob swings from point I to pint II along the circular arc.

Chapter 7 Work And Kinetic Energy Q.3CQ
A friend makes the statement, “A force that is always perpendicular to the velocity of a particle does no work on the particle.” Is this statement true or false? If it is hue, state why; if it is false, give a counterexample.
Solution:
True. A force that is always perpendicular to displacement does not have a non-zero component along the direction of motion. As a result, work will not be done on the particle.
Work done W=(F cosθ)d
W is positive if F has a component in the direction of motion.
W is positive if the angle between the force F and displacement d is -90< <90.

Chapter 7 Work And Kinetic Energy Q.3P
A pendulum bob swings from point II to point III along the circular arc indicated in Figure. (a) Is the work done on the bob by gravity positive, negative, or zero? Explain. (b) Is the work done on the bob by the string positive, negative, or zero? Explain.
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy3p

Solution:
(a) When the pendulum bob swings from point II to point III along the circular arc, its displacement is upward. This is opposite to the direction of force of gravity. Therefore the work done by the gravity is negative when the pendulum bob swings from point II to pint III along the circular arc.
(b) When the pendulum bob swings from point II to point III along the circular arc, the tension in the string is always perpendicular to its direction of motion. Therefore the work done by the string is zero when the pendulum bob swings from point II to pint III along the circular arc.

Chapter 7 Work And Kinetic Energy Q.4CQ
The net work done on a certain object is zero. What can you say about its speed?
Solution:
The work done is equal to the change in kinetic energy. So if the net work done on an object is zero, its change in kinetic energy is also zero. Thus, the speed of the object will remain the same.
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy4cqps

Chapter 7 Work And Kinetic Energy Q.4P
A farmhand pushes a 26-kg bale of hay 3.9 m across the floor of a barn. If she exerts a horizontal force of 88 N on the hay, how much work has she done?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy4ps

Chapter 7 Work And Kinetic Energy Q.5CQ
To get out of bed in the morning, do you have to do work? Explain.
Solution:
Yes, we have to do work against the force of gravity to get out of bed in the morning because the constant force of gravity acts downward on our body when we are sleeping in bed. To get up we have to apply force upward; thus, we are doing work against the force of gravity.

Chapter 7 Work And Kinetic Energy Q.5P
Children in a tree house lift a small dog in a basket 4.70 m up to their house. If it takes 201 J of work to do this, what is the combined mass of the dog and basket?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy5ps

Chapter 7 Work And Kinetic Energy Q.6CQ
Give an example of a frictional force doing negative work.
Solution:
Frictional forces do negative work whenever they act in a direction that opposes the motion.
For example, friction does negative work when you push a box across the floor, or when you hit the brakes while driving.

Chapter 7 Work And Kinetic Energy Q.6P
Early one October, you go to a pumpkin patch to select your Halloween pumpkin. You lift the 3.2-kg pumpkin to a height of 1.2 in, then carry it 50.0 m (on level ground) to the check-out stand. (a) Calculate the work you do on the pumpkin as you lift it from the ground. (b) How much work do you do on the pumpkin as you carry it from the field?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy6ps

Chapter 7 Work And Kinetic Energy Q.7CQ
Give an example of a frictional force doing positive work.
Solution:
The force of friction always opposes relative motion, but if the body moves along the direction of applied force, for ◊ = 0º, the work done is positive.
So when man walks on the ground, the frictional force between his shoes and the ground does positive work whenever he begins to walk, as ◊ = 0º.

Chapter 7 Work And Kinetic Energy Q.7P
The coefficient of kinetic friction between a suitcase and the floor is 0.272. If the suitcase has a mass of 71.5 kg, how far can it be pushed across the level floor with 642 J of work?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy7ps

Chapter 7 Work And Kinetic Energy Q.8CQ
A ski boat moves with constant velocity. Is the net force acting on the boat doing work? Explain.
Solution:
Since the velocity of the boat is constant, there will not be any change in the kinetic energy of the boat.
Thus, the change in kinetic energy = 0 joules ————- (1)
Work done = change in kinetic energy —————- (2)
From equations (1) and (2),
work done = 0 joules ——————– (3)
Work done = net force displacement ————— (4)
Since the boat is moving at a constant speed, then from equations (3) and (4),
net force = 0 newtons
Thus, the net force is not doing any work on the boat.

Chapter 7 Work And Kinetic Energy Q.8P
You pick up a 3.4-kg can of paint from the ground and lift it to a height of 1.8 m. (a) How much work do you do on the can of paint? (b) You hold the can stationary for half a minute, waiting for a friend on a ladder to take it. How much work do you do during this time? (c) Your friend decides against the paint, so you lower it back to the ground. How much work do you do on the can as you lower it?
Solution:
Mass of the can m = 3.4 kg
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy8ps

Chapter 7 Work And Kinetic Energy Q.9CQ
A package rests on the floor of an elevator that is rising with constant speed. The elevator exerts an upward normal force on the package, and hence does positive work on it. Why doesn’t the kinetic energy of the package increase?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy9cqs

Chapter 7 Work And Kinetic Energy Q.9P
A tow rope, parallel to the water, pulls a water skier directly behind the boat with constant velocity for a distance of 65 m before the skier falls. The tension in the rope is 120 N. (a) Is the work done on the skier by the rope positive, negative, or zero? Explain. (b) Calculate the work done by the rope on the skier.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy9ps

Chapter 7 Work And Kinetic Energy Q.10CQ
An object moves with constant velocity. Is it safe to conclude that no force acts on the object? Why, or why not?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy10cqs

Chapter 7 Work And Kinetic Energy Q.10P
In the situation described in the previous problem, (a) is the work done on the boat by the rope positive, negative, or zero? Explain. (b) Calculate the work done by the rope on the boat.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy10ps

Chapter 7 Work And Kinetic Energy Q.11CQ
Engine 1 does twice the work of engine 2. Is it correct to conclude that engine 1 produces twice as much power as engine 2? Explain.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy11cqs
The power produced is defined as the rate of the work done. Here it is mentioned that engine 1 does twice the amount of work as engine 2 but their individual time of doing that work is not specified.
Hence, it is incorrect to conclude that engine 1 produces twice the amount of power as produced by engine 2.

Chapter 7 Work And Kinetic Energy Q.11P
A child pulls a friend in a little red wagon with constant speed. If the child pulls with a force of 16 N for 10.0 m, and the handle of the wagon is inclined at an angle of 25° above the horizontal, how much work does the child do on the wagon?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy11ps

Chapter 7 Work And Kinetic Energy Q.12CQ
Engine 1 produces twice the power of engine 2. Is it correct to conclude that engine 1 does twice as much work as engine 2? Explain.
Solution:
No.
Power depends both on the amount of work done by the engine, and the amount of time during which the work is performed.

Chapter 7 Work And Kinetic Energy Q.12P
A 51-kg packing crate is pulled with constant speed across a rough floor with a rope that is at an angle of 43.5° above the horizontal. If the tension in the rope is 115 N, how much work is done on the crate to move it 8.0 m?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy12ps

Chapter 7 Work And Kinetic Energy Q.13P
To clean a floor, a janitor pushes on a mop handle with a force of 50.0 N. (a) If the mop handle is at an angle of 55° above the horizontal, how much work is required to push the mop 0.50 m? (b) If the angle the mop handle makes with the horizontal is increased to 65°, does the work done by the janitor increase, decrease, or stay the same? Explain.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy13ps

Chapter 7 Work And Kinetic Energy Q.14P
A small plane tows a glider at constant speed and altitude. If the plane does 2.00 × 105 J of work to tow the glider 145 m and the tension in the tow rope is 2560 N, what is the angle between the tow rope and the horizontal?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy14ps

Chapter 7 Work And Kinetic Energy Q.15P
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy15p
Solution:

Chapter 7 Work And Kinetic Energy Q.16P
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy16p
Solution:

Chapter 7 Work And Kinetic Energy Q.17P
Water skiers often ride to one side of the center line of a boat, as shown in Figure. In this case, the ski boat is traveling at 15 m/s and the tension in the rope is 75 N. If the boat does 3500 J of work on the skier in 50.0 m, what is the angle θ between the tow rope and the center line of the boat?
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy17p
Solution:

Chapter 7 Work And Kinetic Energy Q.18P
A pitcher throws a ball at 90 mi /h and the catcher stops it in her glove. (a) Is the work done on the ball by the pitcher positive, negative, or zero? Explain. (b) Is the work done on the ball by the catcher positive, negative, or zero? Explain.
Solution:
a) The pitcher does positive work on the ball because the direction of force is along the direction of displacement of the ball.
b) The catcher does negative work on the ball by exerting a force in the direction opposite to the motion of the ball, in order to stop the ball.

Chapter 7 Work And Kinetic Energy Q.19P
How much work is needed for a 73-kg runner to accelerate from rest to 7.7 m/s?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy19ps

Chapter 7 Work And Kinetic Energy Q.20P
Skylab’s Reentry When Skylab reentered the Earth’s atmosphere on July 11, 1979, it broke into a myriad of pieces. One of the largest fragments was a I770-kg lead-lined film vault, and it landed with an estimated speed of 120 m/s. What was the kinetic energy of the film vault when it landed?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy20ps

Chapter 7 Work And Kinetic Energy Q.21P
A 9.50-g bullet has a speed of 1.30 km/s. (a) What is its kinetic energy in joules? (b) What is the bullet’s kinetic energy if its speed is halved? (c) If its speed is doubled?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy21ps

Chapter 7 Work And Kinetic Energy Q.22P
The work W0 accelerates a car from 0 to 50 km/h. (a) Is the work required to accelerate the car from 50 km/h to 150 km/h equal to 2W0, 3W0, 8W0, or 91w0? (b) Choose the best explanation from among the following:
I. The work to accelerate the car depends on the speed squared.
II. The final speed is three times the speed that was produced by the work W0.
III. The increase in speed from 50 km/h to 150 km/h is twice the increase in speed from 0 to 50 km/h.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy22ps

Chapter 7 Work And Kinetic Energy Q.23P
Jogger A has a mass m and a speed v, jogger B has a mass m/2 and a speed 3v, jogger C has a mass 3m and a speed v/2, and jogger D has a mass 4m and a speed v/2. Rank the joggers in order of increasing kinetic energy. Indicate ties where appropriate.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy23ps
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Chapter 7 Work And Kinetic Energy Q.24P
A 0.14-kg pinecone falls 16 m to the ground, where it lands with a speed of 13 m/s. (a) With what speed would the pinecone have landed if there had been no air resistance? (b) Did air resistance do positive work, negative work, or zero work on the pinecone? Explain.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy24ps

Chapter 7 Work And Kinetic Energy Q.25P
In the previous problem, (a) how much work was done on the pinecone by air resistance? (b) What was the average force of air resistance exerted on the pinecone?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy25ps
The negative sign indicates that the force acts in the upward direction.

Chapter 7 Work And Kinetic Energy Q.26P
At t = 1.0 s, a 0.40-kg object is falling with a speed of 6.0 m/s. At t = 2.0 s, it has a kinetic energy of 25 J. (a) What is the kinetic energy of the object at t = 1.0 s? (b) What is the speed of the object at t = 2.0 s? (c) How much work was done on the object between t = 1.0 s and t = 2.0 s?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy26ps

Chapter 7 Work And Kinetic Energy Q.27P
After hitting a long fly ball that goes over the right fielder’s head and lands in the outfield, the batter decides to keep going past second base and try for third base. The 62.0-kg player begins sliding 3.40 m from the base with a speed of 4.35 m/s. If the player comes to rest at third base, (a) how much work was done on the player by friction? (b) What was the coefficient of kinetic friction between the player and the ground?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy27ps

Chapter 7 Work And Kinetic Energy Q.28P
A 1100-kg car coasts on a horizontal road with a speed of 19 m/s. After crossing an unpaved, sandy stretch of road 32 m long, its speed decreases to 12 m/s. (a) Was the net work done on the car positive, negative, or zero? Explain. (b) Find the magnitude of the average net force on the car in the sandy section.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy28ps

Chapter 7 Work And Kinetic Energy Q.29P
(a) In the previous problem, the car’s speed decreased by 7.0 m/s as it coasted across a sandy section of road 32 m long. If the sandy portion of the road had been only 16 m long, would the car’s speed have decreased by 3.5 m/s, more than 3.5 m/s, or less than 3.5 m/s? Explain. (b) Calculate the change in speed in this case.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy29ps

Chapter 7 Work And Kinetic Energy Q.30P
A 65-kg bicyclist rides his 8.8-kg bicycle with a speed of 14 m/s. (a) How much work must be done by the brakes to bring the bike and rider to a stop? (b) How far does the bicycle travel if it takes 4.0 s to come to rest? (c) What is the magnitude of the braking force?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy30ps

Chapter 7 Work And Kinetic Energy Q.31P
A block of mass m and speed v collides with a spring, compressing it a distance △x. What is the compression of the spring if the force constant of the spring is increased by a factor of four?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy31ps

Chapter 7 Work And Kinetic Energy Q.32P
A spring with a force constant of 3.5 × 104 N/m is initially at its equilibrium length. (a) How much work must you do to stretch the spring 0.050 m? (b) How much work must you do to compress it 0.050 m?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy32ps

Chapter 7 Work And Kinetic Energy Q.33P
A 1.2-kg block is held against a spring of force constant 1.0 × 104 N/m, compressing it a distance of 0.15 m. How fast is the block moving after it is released and the spring pushes it away?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy33ps

Chapter 7 Work And Kinetic Energy Q.34P
Initially sliding with a speed of 2.2 m/s, a 1.8-kg block collides with a spring and compresses it 0.31 m before coming to rest. What is the force constant of the spring?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy34ps

Chapter 7 Work And Kinetic Energy Q.35P
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy35p
Solution:

Chapter 7 Work And Kinetic Energy Q.36P
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy36p
Solution:

Chapter 7 Work And Kinetic Energy Q.37P
CE A block of mass m and speed v collides with a spring, compressing it a distance △x. What is the compression of the spring if the mass of the block is halved and its speed is doubled?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy37ps

Chapter 7 Work And Kinetic Energy Q.38P
To compress spring 1 by 0.20 m takes 150 J of work. Stretching spring 2 by 0.30 m requires 210 J of work. Which spring is stiffer?
Solution:
38ps
Work done to compress spring 1 by x = 0.2 m is W = 150 J We know that
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy38ps

Chapter 7 Work And Kinetic Energy Q.39P
It takes 180 J of work to compress a certain spring 0.15 m. (a) What is the force constant of this spring? (b) To compress the spring an additional 0.15 m, does it take 180 J, more than 180 J, or less than 180 J? Verify your answer with a calculation.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy39ps

Chapter 7 Work And Kinetic Energy Q.40P
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy40p
Solution:

Chapter 7 Work And Kinetic Energy Q.41P
A block is acted on by a force that varies as (2.0 × 104 N/m)x for 0 ≤ x ≤ 0.21 m, and then remains constant at 4200 N for larger x. How much work does the force do on the block in moving it (a) from x = 0 to x = 0.30 m, or (b) from x = 0.10 m to x = 0.40 m?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy41ps

Chapter 7 Work And Kinetic Energy Q.42P
CE Force F1 does 5 J of work in 10 seconds, force F2 does 3 J of work in 5 seconds, force F3 does 6 J of work in 18 seconds, and force F4 does 25 J of work in 125 seconds. Rank these forces in order of increasing power they produce. Indicate ties where appropriate.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy42ps

Chapter 7 Work And Kinetic Energy Q.43P
Climbing the Empire State Building A new record for running the stairs of the Empire State Building was set on February 3, 2003. The 86 flights, with a total of 1576 steps, was run in 9 minutes and 33 seconds. If the height gain of the step was 0.20 m, and the mass of the runner was 70.0 kg, what was his average power output during the climb? Give your answer in both watts and horsepower.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy43ps

Chapter 7 Work And Kinetic Energy Q.44P
How many joules of energy are in a kilowatt-hour?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy44ps

Chapter 7 Work And Kinetic Energy Q.45P
Calculate the power output of a 1.4-g fly as it walks straight tip a windowpane at 2.3 cm/s.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy45ps

Chapter 7 Work And Kinetic Energy Q.46P
An ice cube is placed in a microwave oven. Suppose the oven delivers 105 W of power to the ice cube and that it takes 32,200 J to melt it. How long docs it take for the ice cube to melt?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy46ps

Chapter 7 Work And Kinetic Energy Q.47P
You raise a bucket of water from the bottom of a deep well. If your power output is 108 W, and the mass of the bucket and the water in it is 5.00 kg, with what speed can you raise the bucket? Ignore the weight of the rope.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy47ps

Chapter 7 Work And Kinetic Energy Q.48P
In order to keep a leaking ship from sinking, it is necessary to pump 12.0 lb of water the second from below deck up a height of 2.00 m and over the side. What is the minimum horse power motor that can be used to save the ship?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy48ps

Chapter 7 Work And Kinetic Energy Q.49P
A kayaker paddles with a power output of 50.0 W to maintain a steady speed of 1.50 m/s. (a) Calculate the resistive force exerted by the water on the kayak. (b) If the kayaker doubles her power output, and the resistive force due to the water remains the same, by what factor does the kayaker’s speed change?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy49ps

Chapter 7 Work And Kinetic Energy Q.50P
Human-Powered Flight Human-powered aircraft re quire a pilot to pedal, as in a bicycle, and produce a sustained power output of about 0.30 hp. The Gossamer Albatross flew across the English Channel on June 12, 1979, in 2 h 49 min. (a) How much energy did the pilot expend during the flight? (b) How many Snickers candy bars (280 Cal per bar) would the pilot have to consume to be “fueled up” for the flight? [Note: The nutritional calorie, 1 Cal, is equivalent to 1000 calories (1000 cal) as defined in physics. In addition, the conversion factor between calories and joules is as follows: 1 Cal = 1000 cal = 1 kcal = 4186 J.]
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy50ps

Chapter 7 Work And Kinetic Energy Q.51P
A grandfather clock is powered by the descent of a 4.35-kg weight. (a) If the weight descends through a distance of 0.760 m in 3.25 days, how much power docs it deliver to the clock? (b) To increase the power delivered to the clock, should the time it takes for the mass to descend be increased or decreased? Explain.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy51ps

Chapter 7 Work And Kinetic Energy Q.52P
The Power You Produce Estimate the power you produce in running up a flight of stairs. Give your answer in horsepower.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy52ps

Chapter 7 Work And Kinetic Energy Q.53P
A certain car can accelerate from rest to the speed v in T seconds. If the power output of the car remains constant, (a) how long does it take for the car to accelerate from v to 2v? (b) How fast is the car moving at 2T seconds after starting?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy53ps

Chapter 7 Work And Kinetic Energy Q.54GP
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy54p
Solution:

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Chapter 7 Work And Kinetic Energy Q.55GP
A youngster rides on a skateboard with a speed of 2 m/s. After a force acts on the youngster, her speed is 3 m/s. Was the work done by the force positive, negative, or zero? Explain.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy55gps

Chapter 7 Work And Kinetic Energy Q.56GP
Predict/Explain A car is accelerated by a constant force, F. The distance required to accelerate the car from rest to the speed v is △x. (a) Is the distance required to accelerate the car from the speed v to the speed 2v equal to △x, 2△x, 3△x, or 4△x? (b) Choose the best explanation from among the following:
I. The final speed is twice the initial speed.
II. The increase in speed is the same in each case.
III. Work is force times distance, and work depends on the speed squared.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy56gps

Chapter 7 Work And Kinetic Energy Q.57GP
Car 1 has four times the mass of car 2, but they both have the same kinetic energy. If the speed of car 2 is v, is the speed of car 1 equal to v/4, v/2, 2v, or 4v? Explain.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy57gps

Chapter 7 Work And Kinetic Energy Q.58GP
Muscle Cells Biological muscle cells can be thought of as nanomotors that use the chemical energy of ATP to produce mechanical work. Measurements show that the active proteins within a muscle cell (such as myosin and actin) can produce a force of about 7.5 pN and displacements of 8.0 run. How much work is done by such proteins?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy58gps

Chapter 7 Work And Kinetic Energy Q.59GP
When you take a bite out of an apple, you do about 19 J of work. Estimate (a) the force and (b) the power produced by your jaw muscles during the bite.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy59gps

Chapter 7 Work And Kinetic Energy Q.60GP
A Mountain bar has a mass of 0.045 kg and a calorie rating of 210 Cal. What speed would this candy bar have if its kinetic energy were equal to its metabolic energy? [See the note following Problem.]
Human-Powered Flight Human-powered aircraft re quire a pilot to pedal, as in a bicycle, and produce a sustained power output of about 0.30 hp. The Gossamer Albatross flew across the English Channel on June 12, 1979, in 2 h 49 min. (a) How much energy did the pilot expend during the flight? (b) How many Snickers candy bars (280 Cal per bar) would the pilot have to consume to be “fueled up” for the flight? [Note: The nutritional calorie, 1 Cal, is equivalent to 1000 calories (1000 cal) as defined in physics. In addition, the conversion factor between calories and joules is as follows: 1 Cal = 1000 cal = 1 kcal = 4186 J.]
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy60gps

Chapter 7 Work And Kinetic Energy Q.61GP
A small motor runs a lift that raises a load of bricks weighing 836 N to a height of 10.7 m in 23.2 s. Assuming that the bricks are lifted with constant speed, what is the minimum power the motor must produce?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy61gps

Chapter 7 Work And Kinetic Energy Q.62GP
You push a 67-kg box across a floor where the coefficient of kinetic friction is µk = 0.55. The force you exert is horizontal. (a) How much power is needed to push the box at a speed of 0.50 m/s? (b) How much work do you do if you push the box for 35 s?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy62gps

Chapter 7 Work And Kinetic Energy Q.63GP
The Beating Heart The average power output of the human heart is 1.33 watts. (a) How much energy does the heart produce in a day? (b) Compare the energy found in part (a) with the energy required to walk up a flight of stairs. Estimate the height a person could attain on a set of stairs using nothing more than the daily energy produced by the heart.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy63gps

Chapter 7 Work And Kinetic Energy Q.64GP
The Atmos Clock The Atmos clock (the so-called perpetual motion clock) gets its name from the fact that it runs off pressure variations in the atmosphere, which drive a bellows containing a mixture of gas and liquid ethyl chloride. Because the power to drive these clocks is so limited, they must be very efficient. In fact, a single 60.0-W lightbulb could power 240 million Atmos clocks simultaneously. Find the amount of energy, in joules, required to run an Atmos clock for one day.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy64gps

Chapter 7 Work And Kinetic Energy Q.65GP
The work W0 is required to accelerate a car from rest to the speed v0. How much work is required to accelerate the car (a) from rest to the speed v0/2 and (b) from v0/2 to v0?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy65gps

Chapter 7 Work And Kinetic Energy Q.66GP
A work W0 is required to stretch a certain spring 2 cm from its equilibrium position. (a) How much work is required to stretch the spring 1 cm from equilibrium? (b) Suppose the spring is already stretched 2 cm from equilibrium. How much additional work is required to stretch it to 3 cm from equilibrium?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy66gps

Chapter 7 Work And Kinetic Energy Q.67GP
After a tornado, a 0.55-g straw was found embedded 2.3 cm into the trunk of a tree. If the average force exerted on the straw by the tree was 65 N, what was the speed of the straw when it hit the tree?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy67gps

Chapter 7 Work And Kinetic Energy Q.68GP
You throw a glove straight upward to celebrate a victory. Its initial kinetic energy is K and it reaches a maximum height h. What is the kinetic energy of the glove when it is at the height h/2?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy68gps

Chapter 7 Work And Kinetic Energy Q.69GP
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy69gp
Solution:

Chapter 7 Work And Kinetic Energy Q.70GP
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy70gp
Solution:

(C) If the pulling force remains the e, then the work done remains the e. If the increased mass results in a larger friction force and an increase in the pulling force, then the work done increases.

Chapter 7 Work And Kinetic Energy Q.71GP
A 0.19-kg apple falls from a branch 3.5 m above the ground. (a) Does the power delivered to the apple by gravity increase, de crease, or stay the same during the time the apple falls to the ground? Explain. Find the power delivered by gravity to the apple when the apple is (b) 2.5 m and (c) 1.5 m above the ground.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy71ps

Chapter 7 Work And Kinetic Energy Q.72GP
A juggling ball of mass m is thrown straight upward from an initial height h with an initial speed v0. How much work has gravity done on the ball (a) when it reaches its greatest height, h max, and (b) when it reaches ground level? (c) Find an expression for the kinetic energy of the ball as it lands.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy72ps

Chapter 7 Work And Kinetic Energy Q.73GP
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy73p
Solution:

Chapter 7 Work And Kinetic Energy Q.74GP
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy74p
Solution:

Chapter 7 Work And Kinetic Energy Q.75GP
The motor of a ski boat produces a power of 36,600 W to maintain a constant speed of 14.0 m/s. To pull a water skier at the same constant speed, the motor must produce a power of 37,800 W. What is the tension in the rope pulling the skier?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy75ps

Chapter 7 Work And Kinetic Energy Q.76GP
Cookie Power To make a batch of cookies, you mix half a bag of chocolate chips into a bowl of cookie dough, exerting a 21-N force on the stirring spoon. Assume that your force is always in the direction of motion of the spoon. (a) What power is needed to move the spoon at a speed of 0.23 m/s? (b) How much work do you do if you stir the mixture for 1.5 min?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy76gps

Chapter 7 Work And Kinetic Energy Q.77GP
A pitcher accelerates a 0.14-kg hardball from rest to 42.5 m/s in 0.060 s. (a) How much work does the pitcher do on the ball? (b) What is the pitcher’s power output during the pitch? (c) Suppose the ball reaches 42.5 m/s in less than 0.060 s. Is the power produced by the pitcher in this case more than, less than, or the same as the power found in part (b)? Explain.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy77gps

Chapter 7 Work And Kinetic Energy Q.78GP
Catapult Launcher A catapult launcher on an aircraft carrier accelerates a jet from rest to 72 m/s. The work done by the catapult during the launch is 7.6 × 107 J. (a) What is the mass of the jet? (b) If the jet is in contact with the catapult for 2.0 s, what is the power output of the catapult?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy78gps

Chapter 7 Work And Kinetic Energy Q.79GP
Brain Power The human brain consumes about 22 W of power under normal conditions, though more power may be required during exams. (a) How long can one Snickers bar (see the note following Problem) power the normally functioning brain? (b) At what rate must you lift a 3.6-kg container of milk (one gallon) if the power output of your arm is to be 22 W? (c) How long does it take to lift the milk container through a distance of 1.0 m at this rate?
Human-Powered Flight Human-powered aircraft re quire a pilot to pedal, as in a bicycle, and produce a sustained power output of about 0.30 hp. The Gossamer Albatross flew across the English Channel on June 12, 1979, in 2 h 49 min. (a) How much energy did the pilot expend during the flight? (b) How many Snickers candy bars (280 Cal per bar) would the pilot have to consume to be “fueled up” for the flight? [Note: The nutritional calorie, 1 Cal, is equivalent to 1000 calories (1000 cal) as defined in physics. In addition, the conversion factor between calories and joules is as follows: 1 Cal = 1000 cal = 1 kcal = 4186 J.]
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy79gps

Chapter 7 Work And Kinetic Energy Q.80GP
A 1300-kg car delivers a constant 49 hp to the drive wheels. We assume the car is traveling on a level road and that all fractional forces may be ignored. (a) What is the acceleration of this car when its speed is 14 m/s? (b) If the speed of the car is doubled, does its acceleration increase, decrease, or stay the same? Explain. (c) Calculate the car’s acceleration when its speed is 28 m/s.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy80gps

Chapter 7 Work And Kinetic Energy Q.81GP
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy81gp
Solution:

Chapter 7 Work And Kinetic Energy Q.82GP
Powering a Pigeon A pigeon in flight experiences a force of air resistance given approximately by F = bv2, where v is the flight speed and b is a constant. (a) What are the units of the constant b? (b) What is the largest possible speed of the pigeon if its maximum power output is P? (c) By what factor does the largest possible speed increase if the maximum power is doubled?
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy82gps

Chapter 7 Work And Kinetic Energy Q.83GP
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy83gp
Solution:

Chapter 7 Work And Kinetic Energy Q.84GP
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy84gp
Solution:

Chapter 7 Work And Kinetic Energy Q.85GP
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy85gp
Solution:

Chapter 7 Work And Kinetic Energy Q.86PP
Microraptor gui: The Biplane Dinosaur
The evolution of flight is a subject of intense interest in paleontology. Some subscribe to the “cursorial” (or ground-up) hypothesis, in which flight began with ground-dwelling animals running and jumping after prey. Others favor the “arboreal” (or trees-down) hypothesis, in which tree-dwelling animals, like modern-day flying squirrels, developed flight as an extension of gliding from tree to tree.
A recently discovered fossil from the Cretaceous period in China supports the arboreal hypothesis and adds a new element—it suggests that feathers on both the wings and the lower legs and feet allowed this dinosaur, Microraptor gui, to glide much like a biplane, as shown in Figure. Re searchers have produced a detailed computer simulation of Microraptor, and with its help have obtained the power-versus-speed plot presented in Figure. This curve shows how much power is required for flight at speeds between 0 and 30 m/s. Notice that the power increases at high speeds, as expected, but is also high for low speeds, where the dinosaur is almost hovering. A minimum of 8.1 W is needed for flight at 10 m/s. The lower horizontal line shows the estimated 9.8-W power output of Microraptor, indicating the small range of speeds for which flight would be possible. The upper horizontal line shows the wider range of flight speeds that would be available if Microraptor were able to produce 20 W of power.
Also of interest are the two dashed, straight lines labeled 1 and 2. These lines represent constant ratios of power to speed; that is, a constant value for P/v. Referring to Equation 7-13, we see that P/v = Fv/v = F, so the lines 1 and 2 correspond to lines of constant force. Line 2 is interesting in that it has the smallest slope that still touches the power-versus-speed curve.
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy86gp

Solution:
From the given figure it is clear that the range of flight speeds for power out put of 9.8W is 7.7m/s to 15m/s
So, option B. is correct.

Chapter 7 Work And Kinetic Energy Q.87PP
Microraptor gui: The Biplane Dinosaur
The evolution of flight is a subject of intense interest in paleontology. Some subscribe to the “cursorial” (or ground-up) hypothesis, in which flight began with ground-dwelling animals running and jumping after prey. Others favor the “arboreal” (or trees-down) hypothesis, in which tree-dwelling animals, like modern-day flying squirrels, developed flight as an extension of gliding from tree to tree.
A recently discovered fossil from the Cretaceous period in China supports the arboreal hypothesis and adds a new element—it suggests that feathers on both the wings and the lower legs and feet allowed this dinosaur, Microraptor gui, to glide much like a biplane, as shown in Figure. Re searchers have produced a detailed computer simulation of Microraptor, and with its help have obtained the power-versus-speed plot presented in Figure. This curve shows how much power is required for flight at speeds between 0 and 30 m/s. Notice that the power increases at high speeds, as expected, but is also high for low speeds, where the dinosaur is almost hovering. A minimum of 8.1 W is needed for flight at 10 m/s. The lower horizontal line shows the estimated 9.8-W power output of Microraptor, indicating the small range of speeds for which flight would be possible. The upper horizontal line shows the wider range of flight speeds that would be available if Microraptor were able to produce 20 W of power.
Also of interest are the two dashed, straight lines labeled 1 and 2. These lines represent constant ratios of power to speed; that is, a constant value for P/v. Referring to Equation 7-13, we see that P/v = Fv/v = F, so the lines 1 and 2 correspond to lines of constant force. Line 2 is interesting in that it has the smallest slope that still touches the power-versus-speed curve.
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy87gp

Solution:
From the figure it is clear that the approximate range of flight speeds would be possible if Microraptor gui could produce 20W of power is 2.5m/s to 25m/s.
This is because below 2.5m/s and above 25m/s, the power out put is greater than 20W.
Therefore option C. is correct.

Chapter 7 Work And Kinetic Energy Q.88PP
Microraptor gui: The Biplane Dinosaur
The evolution of flight is a subject of intense interest in paleontology. Some subscribe to the “cursorial” (or ground-up) hypothesis, in which flight began with ground-dwelling animals running and jumping after prey. Others favor the “arboreal” (or trees-down) hypothesis, in which tree-dwelling animals, like modern-day flying squirrels, developed flight as an extension of gliding from tree to tree.
A recently discovered fossil from the Cretaceous period in China supports the arboreal hypothesis and adds a new element—it suggests that feathers on both the wings and the lower legs and feet allowed this dinosaur, Microraptor gui, to glide much like a biplane, as shown in Figure. Re searchers have produced a detailed computer simulation of Microraptor, and with its help have obtained the power-versus-speed plot presented in Figure. This curve shows how much power is required for flight at speeds between 0 and 30 m/s. Notice that the power increases at high speeds, as expected, but is also high for low speeds, where the dinosaur is almost hovering. A minimum of 8.1 W is needed for flight at 10 m/s. The lower horizontal line shows the estimated 9.8-W power output of Microraptor, indicating the small range of speeds for which flight would be possible. The upper horizontal line shows the wider range of flight speeds that would be available if Microraptor were able to produce 20 W of power.
Also of interest are the two dashed, straight lines labeled 1 and 2. These lines represent constant ratios of power to speed; that is, a constant value for P/v. Referring to Equation 7-13, we see that P/v = Fv/v = F, so the lines 1 and 2 correspond to lines of constant force. Line 2 is interesting in that it has the smallest slope that still touches the power-versus-speed curve.
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy88gp

Solution:

Chapter 7 Work And Kinetic Energy Q.89PP
Microraptor gui: The Biplane Dinosaur
The evolution of flight is a subject of intense interest in paleontology. Some subscribe to the “cursorial” (or ground-up) hypothesis, in which flight began with ground-dwelling animals running and jumping after prey. Others favor the “arboreal” (or trees-down) hypothesis, in which tree-dwelling animals, like modern-day flying squirrels, developed flight as an extension of gliding from tree to tree.
A recently discovered fossil from the Cretaceous period in China supports the arboreal hypothesis and adds a new element—it suggests that feathers on both the wings and the lower legs and feet allowed this dinosaur, Microraptor gui, to glide much like a biplane, as shown in Figure. Re searchers have produced a detailed computer simulation of Microraptor, and with its help have obtained the power-versus-speed plot presented in Figure. This curve shows how much power is required for flight at speeds between 0 and 30 m/s. Notice that the power increases at high speeds, as expected, but is also high for low speeds, where the dinosaur is almost hovering. A minimum of 8.1 W is needed for flight at 10 m/s. The lower horizontal line shows the estimated 9.8-W power output of Microraptor, indicating the small range of speeds for which flight would be possible. The upper horizontal line shows the wider range of flight speeds that would be available if Microraptor were able to produce 20 W of power.
Also of interest are the two dashed, straight lines labeled 1 and 2. These lines represent constant ratios of power to speed; that is, a constant value for P/v. Referring to Equation 7-13, we see that P/v = Fv/v = F, so the lines 1 and 2 correspond to lines of constant force. Line 2 is interesting in that it has the smallest slope that still touches the power-versus-speed curve.
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy89gp

Solution:

Chapter 7 Work And Kinetic Energy Q.90IP
Referring to Figure Suppose the block has a mass of 1.4 kg and an initial speed of 0.62 m/s. (a) What force constant must the spring have if the maximum compression is to be 2.4 cm? (b) If the spring has the force constant found in part (a), find the maximum compression if the mass of the block is doubled and its initial speed is halved.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy90ips

Chapter 7 Work And Kinetic Energy Q.91IP
Referring to Figure In the situation shown in Figure (d), a spring with a force constant of 750 N/m is compressed by 4.1 cm. (a) If the speed of the block in Figure (f) is 0.88 m/s, what is its mass? (b) If the mass of the block is doubled, is the final speed greater than, less than, or equal to 0.44 m/s? (c) Find the final speed for the case described in part (b).
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy91ips

Chapter 7 Work And Kinetic Energy Q.92IP
Referring to Example Suppose the car has a mass of 1400 kg and delivers 48 hp to the wheels. (a) How long does it take for the car to increase its speed from 15 m/s to 25 m/s? (b) Would the time required to increase the speed from 5.0 m/s to 15 m/s be greater than, less than, or equal to the time found in part (a)? (c) Determine the time required to accelerate from 5.0 m/s to 15 m/s.
Solution:
Mastering Physics Solutions Chapter 7 Work And Kinetic Energy92ips