Conservation of energy for a falling body

Law of conservation of energy - Energy can neither be created nor be destroyed; it can only be transformed from one form to another.

Consider a body of mass m placed at A.

h = AB is the height of the body above the ground

u = 0 is initial velocity at A

v₁ = velocity of body at C

v = velocity of body at B, i.e., just above the ground

(i) At point A

PE_A = mgh

KE_A = 0

Total mechanical energy at A, E_A = PE_A + KE_A = mgh + 0 = mgh

(ii) At point C

v₁²-0 = 2gs

v₁² = 2gs

KE_C =

PE_C = mg(h-s)

Total mechanical energy at C, E_C = PE_C + KE_C = mg(h-s) + mgs = mgh

(iii) At point B

v²-0² = 2gh

v² = 2gh

KE_B =

PE_B = 0

Total mechanical energy at B, E_B = PE_B + KE_B = 0 + mgh= mgh

The total mechanical energy of the body at A, B and C (also at any other point in the path AB) is the same. So, the total mechanical energy of the body throughout the free fall is conserved.