# Kinetic & Potential Energy

**Energy:**

An object possesses energy when it has a capability to do work. Activities like cooking food, dancing on music, singing a song requires energy. Life is impossible without the enrgy. Sun is the biggest natural source of free energy.

An object that possesses energy can exert a force on another object and energy is transferred from the former to the latter. The second object move as it receives energy and therefore do some work. This implies that any object that possesses energy can do work.

Unit of energy = joule

**Forms of energy:**

The various forms of energy includes

· Mechanical energy – Kinetic energy and potential energy

· Heat energy

· Chemical energy

· Electrical energy

· Light energy

**Kinetic energy: **

When object is in motion, it possesses energy that is called as kinetic energy. Activities like riding horse, driving car, rolling stone, flying plane are the examples of kinetic energy. The kinetic energy of an object increases with its speed.

Consider an object of mass m moving with a uniform velocity u. Let is now be displaced through a distance s when a constant force F acts on it in the direction of its displacement. Now, work done on the object is

W = F s -------------------(1)

Work done on the object causes a change in its velocity v and the acceleration of an object is a, then,

………………………(2)

Now force F = ma ………………………(3)

Applying 2 and 3 in equation 1,

IF an object is starting from its stationary position, that is u = 0, then

Equation shows that work done is equal to the change in the kinetic energy of an object (E_{k}).

**Potential energy:**

The potential energy possessed by the object is the energy present in it by virtue of its position or configuration that means potential energy is stored energy in the object when work is done on the object but there is no change in the velocity or speed of the object.

Gravitational potential energy is the energy possess by the object when it is raised against the gravity. It is defined as the work done in raising it from the ground to that point against gravity.

Consider an object of mass m is raised through a height h from the ground. A force is required to do this. The minimum force required to raise the object is equal to the weight of the object mg. The object gains energy equal to the work done on it. Let the work done on the object against gravity be w then,

Work done w = force x displacement

w = mg x h

Since work done on the object is equal to mgh, energy equal to mgh units is gained by the object. This is the potential energy (Ep) of the object.

E_{p }= mgh

Equation shows that the work done by gravity depends on the difference in vertical heights of the initial and final positions of the object and not on the path along which the object is moved

**Law of conservation of energy:**

Total energy of the system remains unchanged when energy is transformed. Energy can neither be created nor destroyed but only converted from one form to another. The total energy before and after the transformation remain the same. This is called as law of conservation of energy.

Consider an object of mass m is made to fall freely from a height h.

At a start, the potential energy = mgh and kinetic energy = zero because its velocity is zero.

Total energy of the object = mgh.

As it falls, its potential energy will change into kinetic energy. If v is the velocity of the object at a given instant, the kinetic energy = 1/2mv^{2}.

As the fall of the object continues, the potential energy would decrease while the kinetic energy would increase.

When the object is about to reach the ground, h = 0 and v will be the highest. Therefore, the kinetic energy would be the largest and potential energy the least. However, the sum of the potential energy and kinetic energy of the object would be the same at all points.

Potential energy + Kinetic energy = constant

mgh + ½ mv^{2} = constant

The sum of kinetic energy and potential energy of an object is its total mechanical energy.

**Calculations:**

Ex-1: If an object is having mass m, moves with velocity v, then kinetic energy of the object is ……..

a) mv b) 1/2 mv c) **1/2 mv**^{2} d) mv^{2}

Answer: Kinetic energy of the object depends on the motion of an object. Work done is equal to the change in the kinetic energy of an object. Here object is moving with velocity v and mass m, so the kinetic energy of the object is 1/2 mv^{2}.

Ex-2: The sum of kinetic energy and the potential energy is called ……………

a) Heat energy

b) Chemical energy

**c) ****Mechanical energy**

d) None

Answer: An object possesses energy when it has a capability to do work.

Ex-3: An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height of the object with respect to the ground. Given g = 10 m/s.

a) 5 m b) 10 m c) **4 m** d) 40 m

Answer:

m = 12 kg

Ep = 480 J

Ep = m g h

h = __480__

12 x 10

h = 4 m