Give one example of each of the following: (i) Small mass but high kinetic energy (ii) Large mass but low kinetic energy (b) Prove mathematically that the total mechanical energy of a freely falling body in air is conserved.

(a) (i) A cricket/hockey ball which has been hit hard and is travelling fast.

(ii) A shot put thrown by an athlete

(b) Let the body of mass m at height h above the ground starting from rest, be falling freely.

Total energy of the body at height h

= mgh (PE) + 0 (KE) = mgh

After the body has fallen freely through a distance x (say),

KE = mgh, PE = mg (h – x)

Total energy = KE + PE

= mgh + mg (h – x) = mgh

When it reaches the ground KE ={1\over2} m.2gh = mgh

PE = 0, Total Energy = KE + PE = mgh

Thus, the total mechanical energy, which is the sum of KE and PE is always equal to mgh.