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Law of Conservation of Energy

When energy is converted from potential energy to kinetic energy, the energy lost in one form reappears in the other. When a body falls, the loss of its potential energy is transformed into kinetic energy till it reaches the ground.

‘Energy can neither be created nor be destroyed. It can be transformed from one form of energy into another in an equivalent amount’. This is known as the law of conservation of energy.

To Verify the Law of Conservation of Energy:

Conservation of Energy

Consider an object of mass ‘m’ at a height h (from the ground). Let ‘g’ be the acceleration due to gravity.

Let us consider the energy possessed by the object at three stages A, B and C.

A is at a height h

B is at a height (h - X)

C is on the ground (ground level)


Energy at A

Object is at rest at a height h.

Potential energy (P.E.) = mgh joule

Kinetic energy (K.E) = 0 (because object is at rest)

Total energy at A = Potential Energy + Kinetic Energy = mgh + 0

Energy at A           = mgh joule


Energy at B

Object is at a height ‘X’ from A and (h - x) from the ground. So it possesses both potential and kinetic energies.

Potential energy = mg (h - x) joule

Kinetic energy = ½ mv2 ------------ (1)

Where ‘v’ is the velocity of the object at B.

According to the third equation of motion, we have V2 = u2 + 2as

Here, u = 0, a = g, s = x

V2 = 2gx -------- (2)

Substituting (2 in (1), we get

Kinetic energy = mg
´ joule

Total energy at B = P.E. + K. E.
                         = mg (h - x) + mgx

                                      = mgh - mgx + mgx

Energy at B         = mgh joule

Energy at C

Since it has struck the ground, the energy is completely kinetic.

P.E. = mgh joule

      = m
´ g ´ 0 = 0; (since h=0)

Potential energy = 0.


According to the third Equation of motion

V2 = u2 + 2as
U  = 0
A  = g
S  = h
V2 = 2gh


Kinetic energy  = ½ mv2 joule

= ½
´ m ´ 2gh = mgh joule

Total energy at C = P.E. + K. E.

                         = 0 + mgh
                         = mgh joule
       Energy at C = mgh joule


At all three stages A, B and C, the total energy is mgh joule. So energy disappears in one form and reappears in another form. If it is lost as potential energy it is transformed into kinetic energy, thus verifying the law of conservation of energy which states that ‘Energy can neither be created nor be destroyed, but can be transformed from one form into another form in an equivalent amount’.


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