Energy can neither be created nor destroyed, but it

is transformed from one form to another. Alternatively,

whenever energy gets transformed, the total energy

remains unchanged.

**Proof – Freely falling body**

It may be shown that in the absence of external frictional force the total mechanical energy of a body remains constant.

Let a body of mass m falls from a point A, which is at a height h from the ground as shown in fig.

**At A,**

Potential energy Ep = mgh

Total energy E = Ep + Ek = mgh + 0= mgh

**At B,**

^{2}= u

^{2}+ 2as

^{2}= 0 + 2ax = 2ax

^{2}= 1/2 m x 2gx = mgx

Potential energy Ep = mg (h – x)

Total energy E = Ep + Ek = mg (h-x) + mgx = mgh – mgx + mgx= mgh

If the body reaches the position C.

**At C,**

Potential energy Ep = 0

Velocity of the body C is

v

^{2}= u

^{2}+ 2as

u = 0, a = g, s = h

applying v

^{2}= 0 + 2gh = 2gh

kinetic energy Ek =1/2 mv

^{2}=1/2 m x 2gh= mgh

Total energy at C

E = Ep + Ek

E = 0 + mgh

E = mgh

*Thus we have seen that sum of potential and kinetic energy of freely falling body at all points remains same. Under the force of gravity, the mechanical energy of a body remains constant.*

__RATE OF DOING WORK (OR) POWER__

*Power is defined as the rate of doing work or work done per unit time.*

^{6 }J

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