INTERCOVERSION OF POTENTIAL AND KINEIC ENERGY

INTERCOVERSION OF POTENTIAL AND KINEIC ENERGY

(i) For a freely falling body, potential energy changes into kinetic energy.

Let a body of mass m be at rest at a point at height (h) from the ground.

At highest point (h) :

Potential energy of the body U₁ = mgh

Kinetic energy of the body K₁ = 0 [u = 0] body is at rest.

As the body falls freely, it gains velocity and reduces height. Let the body have velocity v when it reaches the ground.

At lowest point:

Potential energy of the body,U₂= 0 [h = 0]

Kinetic energy of the body,K₂ =

From third equation of motion, v2 = u2 + 2gh

We have, v2 = 2gh [u = 0]

Hence, final kinetic energy

= mgh = Initial potential energy

(ii) For an upward projected body, kinetic energy changes into potential energy.

Let a body of mass m be projected upwards with a velocity u from a point on the ground.

At lowest point :

Kinetic energy of the body,

Potential energy of the body, U2= 0

As the body rises upward, it gains height and loses velocity.

Let the body reach highest point height h where velocity becomes zero.

At highest point:

Kinetic energy of the body, K2 = 0

Potential energy of the body U2 = mgh

From third equation of motion, v2 = u2 + 2gh

We have 0 = u2 - 2gh

(v = 0 and g is negative for upward motion)

or u2 = 2gh

Hence, final P.E. = mgh = m

P.E. =mu2 = Initial K.E.