Question

State and prove law of conservation of energy in case of a freely falling body.

Answer 1

Law of conservation of energy states that the energy can neither be created nor destroyed but can be transformed from one form to another.

Let us now prove that the above law holds good in the case of a freely falling body.

Let a body of mass 'm' placed at a height 'h' above the ground, start falling down from rest.

In this case we have to show that the total energy (potential energy + kinetic energy) of the body A, B and C remains constant i.e, potential energy is completely transformed into kinetic energy.

Answer 2

Hey mate,

◆ Law of conservation of energy -
- It states that the total energy of an isolated system remains constant.
- This means that energy can neither be created nor destroyed, it can only be transformed or transferred from one form to another.

◆ Proof-
Consider, a body of mass m resting at height h.
Initially it's energies are-
PEi = mgh
KEi = 1/2 mv^2 = 1/2 m×(0)^2 = 0
Total initial energy
Ei = KEi + PEi = mgh

Now, consider it falls freely on the ground-
Using 2nd kinematic eqn-
v'^2 = v^2 + 2as
v'^2 = 0^2 + 2×g×h
v'^2 = 2gh
Finally it's energies are-
PEf = mgh' = mg×0 = 0
KEf = 1/2 mv'^2 = 1/2 × m × 2gh = mgh
Total final energy
Ef = KEf + PEf = mgh

Here, Ei = Ef
Thus total energy is conserved...

Hope this helps you...