Class 9 Science

# Types of Energy

## Kinetic Energy

Kinetic energy is the energy possessed by an object because of its motion. For example, a fast moving pebble can injure a person or break glass pane of window. Energy of moving vehicle, a fast moving wind can damage many house, or wind can move blades of wind mill, etc. All of this is possible because of kinetic energy.

### Drivation of Kinetic Energy

Suppose, the mass of a moving object = m

The initial velocity of a moving object = u

The acceleration of the object = a

The final velocity of the object = v

Displacement of object to achieve the final velocity = s.

We know from the equation of motion that,

v2 = u2 + 2as

Or, 2as = v2 - u2

Or, s=(v^2-u^2)/(2a) -----(i)

Now, we know that, Work done = W = F × s

By substituting the value of s from equation (i) in the expression W = F × s we get

W=Fxx(v^2-u^2)/(2a)

Now, according to Newton’s Second Law of motion, Force = mass × acceleration

Or, F = m × a

Therefore, by substituting the value of F in equation (ii) we get,

W=m×a×(v^2-u^2)/(2a)

=>W=1/2 m(v^2-u^2) ---(iii)

If the object starts moving from the state of rest, then initial velocity (u) will be equal to zero.

Therefore, equation (iii) can be written as

=>W=1/2m(v^2-0^2)

=>W= 1/2 mv^2 ------(iv)

Equation (iv) shows that work done is equal to the change in kinetic energy of an object.

Therefore, if an object of mass m is moving with a constant velocity,

The Kinetic Energy (E_k) = 1/2 mv^2 ----(v)

From the above equation it is clear that kinetic energy of a moving object increases with increase of mass and velocity of the object.

## Potential Energy

Energy possessed by an object because of its position is called potential energy. For example, when a stone is kept at a height, it possesses some energy because of its height. Because of this potential energy, object kept at a height falls over the ground.

A stretched rubber band possesses some energy because of its position. Because of that energy, when the stretched rubber band is released it acquires its original position by movement. A stretched catapulted possesses potential energy because of its stretched string and is able to do some work.

A stretched bow possesses energy because of its position of stretched string.

### Expression for Potential Energy:

Potential energy possessed by an object due to its height

Let and object of mass m is placed over a height, h against gravity.

Therefore, the minimum force required to work done, F = mg

Where, F is force, m is mass and g is the acceleration due to gravity.

We know that, work done = Force × displacement

Therefore, Work done, W = F × h

Where, h is the displacement of the object. Since, the object is displaced at a height, therefore, h is taken at the place of s.

Or, W = mg h (since, F = mg)

The potential energy (Ep) is equal to the work done over the object

Therefore, Ep = mgh

The potential energy of an object depends upon the mass and height (position) of the object and not upon the path.