# LAW OF CONSERVATION OF ENERGY

Oct 03, 2013admin10 Class Physics

**LAW OF CONSERVATION OF ENERGY:**

According to the law of conservation of energy,

**“Energy can neither be created nor it is destroyed, however energy can be converted from one form energy to any other form of energy”.**

**Prove the law of conservation of energy**

**Proof:**

Let us consider an example of a body of mass “m” lying at height above the ground At point A body is at rest so its initial velocity is zero.

Suppose the body is released from height “h” and after covering distance of Mx” it velocity become “V” at Point B Now we check the total energy at point a and b

**Energy Conservation At Point ‘A’**

At point A the velocity of body is zero so its Kinetic energy is zero but it has some Potential energy

Total energy = Kinetic Energy + Potential Energy

T.E = K.E + P.E

T.E = 0 + mgh

T.E = mgh ——– 1

**Energy Conservation at Point ‘B’**

At point B the velocity is “V” so its Kinetic Energy is ½ mv^{2} but now first we calculate V

We have

Vi = 0

S = x

a = g

V = ?

According to 3^{rd} equation of motion

2aS = Vf^{2} – Vi^{2}

2gx = v^{2} – 0^{2}

2gx = v^{2} ————- 2

So

K.E = is ½ mv^{2}

K.E = ½ m 2 gx

K.E = mgx ————– 3

So

Total energy = Kinetic Energy + Potential Energy

T.E = K.E + P.E

T.E = mgx + mg(h – x)

T.E = mgx + mgh – mgx

T.E = mgh 4

Equation 1 and 4 show that the total energy at Point A and B are same so the law of conservation of energy is proved

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