## Mastering Physics Solutions Chapter 9 Linear Momentum And Collisions

**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:**

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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.18CQ**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.19P**

**Solution:**

**Chapter 9 Linear Momentum And Collisions Q.20P**

**Solution:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.42P**

**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:**

**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**

**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:**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.48P**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.51P**

**Solution:**

**Chapter 9 Linear Momentum And Collisions Q.52P**

**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:**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.56P**

**Solution:**

**Chapter 9 Linear Momentum And Collisions Q.57P**

**Solution:**

**Chapter 9 Linear Momentum And Collisions Q.58P**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.69GP**

**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:**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.72GP**

**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:**

**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:**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.76GP**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.83GP**

**Solution:**

**Chapter 9 Linear Momentum And Collisions Q.84GP**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.86GP**

**Solution:**

**Chapter 9 Linear Momentum And Collisions Q.87GP**

**Solution:**

**Chapter 9 Linear Momentum And Collisions Q.88GP**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.90GP**

**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:**

**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:**

**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:**

**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:**

**Chapter 9 Linear Momentum And Collisions Q.95GP**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**

**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:**