Potential Energy.

How to Calculate the Energy Used

by

What is Energy

Definition: Energy is the ability to do work. The amount of energy possessed by a body is equal to the amount of work it can do when its energy is released. Thus, energy is defined as the capacity of doing work. Energy is a scalar quantity and it exists in various forms.

Units of energy: The units of energy are the same as that of work. In SI system, the unit of energy is joule (J). In CGS system, the unit of energy is erg.

  • 1 Joule = 107 ergs
  • Other units of energy in common use are watt-hour and kilowatt hour.
  • 1 watt-hour = 1 watt × 1 hour
    = 1 watt × 60 × 60 sec
    = 3600 J
  • 1 kilowatt-hour (kWh) = 3.6 × 106 Joule
  • Heat energy is usually measured in calorie or kilocalorie such that
    1 calorie = 4.18 J
  • A very small unit of energy is electron volt(eV).
    1 eV = 1.6 × 10-19 J

The energy possessed by a body due to its state of rest or state of motion is called mechanical energy.
Mechanical energy is of two types
(A) Kinetic Energy            (B) Potential Energy.

Principle of Conservation of Energy

  1. Principle of conservation of energy states that energy cannot be created or destroyed but can be changed from one form to another.
  2. The total energy of the universe is constant. The total energy of an isolated system is constant.
  3. Figure shows the transformation of energy from one form to another.
    Principle of Conservation of EnergyPrinciple of Conservation of Energy 1

Principle of Conservation of Energy Experiment

Aim: To study the principle of conservation of energy.
Materials: Ticker tape, a polystyrene sheet, string, a 300 g slotted mass, a pulley, cellophane tape
Apparatus: Ticker timer, a.c. power supply, two retort stands with clamps, trolley, electronic balance, plane
Method:

  1. A friction-compensated plane is arranged as shown in Figure.
  2. The mass of the trolley, m1 is measured with an electronic balance.
  3. A slotted mass of mass, m2 = 300 g is tied to one end of a non-elastic string.
  4. The other end of the string is tied to one end of the trolley.
  5. The string is placed over the pulley and held at 0.5 m above the polystyrene sheet.
  6. The ticker timer is switched on and the slotted mass is released so that it falls downward, pulling the trolley down the runway.
  7. The ticker timer is analysed to determine the final velocity of the trolley.
    Principle of Conservation of Energy 2

Results:
Principle of Conservation of Energy 3
Discussion:

  1. The plane is friction-compensated to minimise energy loss due to friction.
  2. When the slotted mass drops, it loses gravitational potential energy. The trolley and slotted mass gain kinetic energy.
  3. Ideally the gravitational potential energy loss, Ep equals to the kinetic energy gain, Ek. This is in accordance to the principle of conservation of energy.
  4. However, the experimental results shows that Ek is slightly less than Ep. This is because of unavoidable energy loss due to friction of the trolley as well as air friction.

 

How Do You Find The Potential Energy

by

What Is Potential Energy

Potential Energy: Thus the energy possessed by a body by virtue of its position or change in shape is known as potential energy. It is obvious that a body may possess energy even when it is not in motion.

Expression for Potential Energy:

  1. Gravitational potential energy is the energy of an object because of its higher position in the gravitational field.
  2. Figure shows a crane lifting an object. Work is done to lift the object. The object gains an amount of energy that equals to the work done to lift it.
    How Do You Find The Potential Energy
  3. The downward force is equal to the weight of the object, W = mg.
  4. Therefore the force, F needed to lift the box at a uniform velocity is equal to mg.
    Displacement, s = h
    Work done, W = F x s = mgh
  5. Since the work done is transferred to the object as gravitational potential energy, the formula for gravitational potential energy, E is given by:
    Ep = mgh

Inter conversion of Potential Energy and Kinetic Energy

Mechanical Energy of a Freely Falling Body:
Assume, a body of mass m is at rest at a height h from the earth’s surface, as it starts falling, its velocity after travelling a distance x (point B) becomes v and its velocity on the earth’s surface is v’.
Mechanical energy of the body at point A:
EA = Kinetic energy + Potential energy
EA = m(0)2 + mgh
EA = mgh                        ……… (i)
Mechanical energy of the body at point B:
EB = \(\frac { 1 }{ 2 }\) mv2 + mg (h – x)            ……..(ii)
Mechanical-Energy-of-a-Freely-Falling-Body
Mechanical energy of the body at point C:
EC  = \(\frac { 1 }{ 2 }\) m (v’)2 + mg × 0
EC = \(\frac { 1 }{ 2 }\) m (v’)2                   ……..(iv)
Use: EA = EB = EC
Hence, when a body falls freely, its mechanical energy will be constant. That means, the total energy of the body during free fall, remains constant at all positions. However, the form of energy keeps on changing at all points during the motion.
Mechanical-Energy-of-a-Freely-Falling-Body-1

Potential Energy Example Problems With Solutions

Example 1. What will be the potential energy of a body of mass 2 kg kept at a height of 10 m ?
Solution:    The potential energy is given by
U = mgh
Here, m = 2 kg; g = 10 m/s2; h = 10 m
∴ U = 2 × 10 × 10 = 200 J

Example 2. In lifting a mass of 25 kg to a certain height 1250 J energy is utilized. Calculate to what height it has been lifted ? (Take g = 10 m/s2)
Solution:   In lifting a mass through a height h the work done is given by
U = mgh
Here, U = 1250 J; g = 10 m/s2; m = 25 kg
∴ 1250 = 25 × 10 × h
or h = 5 m

Example 3. During a physical exercise, Samad, with a mass of 75 kg, is lifted to a height of 2.1 m. Idris, with a mass of 46 kg, is lifted to a height of 3.2 m.
How Do You Find The Potential Energy 1
Which of the two boys has gained more gravitational potential energy? [g = 9.8 m s-2]
Solution:
For Samad;
Gravitational potential energy,
Ep = 75 x 9.8 x 2.1
= 1543.5 J
For Idris;
Gravitational potential energy,
Ep = 46 x 9.8 x 3.2 P
= 1442.6 J
Therefore, Samad has gained more gravitational potential energy.

Example 4. A lift with its passengers has a total mass of 1350 kg. Calculate the gravitational potential energy gained by the lift by moving upwards to a height of 25 m. [g = 9.8 m s-2J]
Solution:
Mass, m = 1350 kg; Height, h = 25 m Therefore,
Gravitational potential energy,
Ep = mgh
= 1350 x 9.8 x 25 = 330 750 J