1. Energy
Ability to do work is energy. If work is done on the body, energy of the body increases. If work is done by
the body, energy of the body reduces. A cyclist pedals the cycle and does work on cycle, so energy of cycle
and cyclist increases. If Breaks are applied to a vehicle in motion, work is done by vehicle against the force
of friction. So, energy of the vehicle decreases. Thus when work is done, there is exchange of energy. Work
is a process. Body cannot possess 'work', it can possess energy. Unit of energy is also joule. There are many
types of energy, out of which we will study kinetic energy and potential energy.
Kinetic Energy
Suppose a person tries to hit you with a bullet, held in his hand. Another person tries to fire a bullet from his
gun. In which case you would be hurt more ? It is obvious that you are more hurt by bullet fired from gun, as
its speed is more, and so it hurts more. Why is it, so ? It is clear that the bullet having more speed has more
energy. Thus, energy associated with motion is called kinetic energy.
Ability of a body to do work due to its motion is called kinetic energy.
There are two ways to measure kinetic energy of a body moving with velocity v.
(1) A body moving with velocity v, becomes stationary after some time, if force is applied opposite
to its motion. We can calculate work done during this time and calculate kinetic energy.
(2) Work required to be done to make a stationary body, move with velocity v, gives the value of kinetic
energy acquired by it.
In this context, work done by a vehicle moving with some velocity v, when brakes are applied, during the
time in which its velocity reduces to zero, can be calculated. It is clear that if magnitude of v is more, work
done will be more. So, higher the speed, more will be the kinetic energy.
So, now let us obtain an expression for kinetic energy. Suppose a body of mass m is lying stationary on a
frictionless horizontal surface. When a force F acts on it, in time t, it undergoes a displacement s, and
acquires velocity v.
If work done during the process s W,
w = F X s

2. But F = m a
:. W = ma x s
Also V2
- U2
= 2as and taking initial velocity
u = 0, we get V2
= 2 a s
Therefore as = 1/2 V2
So work done from above equation is,
W =1/2 mV2
This equation shows that energy to be given to a stationary body of mass m, so that it can move
with velocity v, is 2nv
2
, which results into its kinetic energy.
Thus, kinetic energy (K) of a body of mass m moving with velocity v can be given by
K= 1/2 mV2
In this context when force F acts on a body moving with initial velocity u if the body acquires velocity v
during displacement s then work done
W = F X s
W = mas
= m (1/2 V2
- 1/2 U2
) ( V2
- U2
= 2 as)
W = ½ mV2
- ½ mU2
Thus, when work is done, there is change in kinetic energy of a body.
Gravitational Force
Path of Moon

3. Now consider the case of uniform circular motion. Since its speed is constant (v = u). Thus, hange in its
kinetic energy is zero. So, work is also zero. Also centripetal force is perpendicular to displacement. So,
work is zero.
Example 1 - A ball of mass 200g is moving with speed 27 km/h. Calculate its kinetic energy.
Solution:-
m = 200 g = 0.2 kg, v = 27 km/h
=27x1000/3600 m/s
= 7.5 m/s
Kinetic Energy K = ?
K= ½ mV2
=1/2 * 0.2* (7.5)2
= 5.625 J
Example 2. Kinetic energy of a car, having mass 1000 kg, is 1,12,500 J. Driver applies brakes when an
obstacle is sighted, and car comes to halt after travelling 100m distance. (Without meeting with an
accident) Calculate frictional force.
Solution
Here work = F s
Initial kinetic energy K0 = 1,12,5001, mass m = 1000 kg, Final kinetic energy K = 0
Distance s = 100 m
Work W = F s and W = K - Ka
.. Fs=K-K0 =0-Ka
.. F(lOO) = 0 - 1,12,500
.. F = -1125N
Work W = change in K.E = K - K0
Here force and displacement are in opposite directions, so force is negative.

4. Potential Energy
Ability of a body to do work due to its position or configuration is known as potential energy of the body.
The concept of potential energy is very important for the force fields like gravitational field, electric field
and magnetic field. Here we will discuss the potential energy of a substance kept in the gravitational field
(gravitational potential energy) only.
Generally potential energy is always mentioned along with reference point. This means that potential energy
is relative. It is impossible to find the absolute value of potential energy. Also changes in potential energy
are more important rather than its absolute value. Generally at reference point potential energy is taken to be
zero.
Potential Energy of an object can be negative also. In which condition Think!!!
Activity : Take an object of 5 kg mass and another object of 10 kg mass. First take the object of 5 kg mass
to 1m, 2m and 3m height. In which case you have to do more work ? Now try to take both the objects to 5m
height. For which object you have to do more work ? Where does the energy spent in doing this work go ?
You must have understood, from the activitygiven above, that when a body is taken to a height we have to
do work against the gravitational force and to do this work we have to spend energy which is stored in the
object in form of potential energy. Value of the potential energy depends on gravitational force acting on a
body (gravitational force acting on a body with larger mass is more) and height. Now let us put this fact in
the form of a formula. Suppose as shown in the figure, potential energy at reference level is zero.
Now on applying a force, having magnitude equal to the gravitational force acting on it, in the opposite
direction, it is moved with constant velocity to a height h. Work done in this case is
W = force x displacement
As magnitude of applied force is equal to magnitude of gravitational force.
Force = mg

5. Work = mg h
Energy spent in doing this work is stored in the body in form of potential energy, so potential energy at
height h from the reference level can be given by the following formula.
U = mgh
Also this gravitational potential energy depends on the height from the reference level.