question_answer

   (a) 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.

Answer:

                  (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),       K.E. = mgh, P.E. = mg (h-x) Work and Energy    135 Total energy = K.E. + P.E. = mgh + mg (h - x) = mgh When it reaches the ground P.E. = 0, Total Energy = K.E. + P.E. = mgh Thus, the total mechanical energy, which is the sum of K.E. and P.E. is always equal to mgh.