Question

Name two examples in which the mechanical energy of a system remains constant.

Answer 1

(1) A body hurled vertically upward under gravity experiences a continuous increase in P.E. and a continuous decrease in KE. The sum of these two quantities at any one time stays constant.

(2) Because of the height h above ground and KE = 0, in the case of a simple pendulum at B, Bob just has P.E.

∴ Sum of P.E. + K.E. = mgh + 0 = mgh

At A the resting position h = 0 and P.E. = 0 but has maximum KE. (Since P.E. has been converted into KE.)

∴ Sum of P.E. and K.E. is same at A as at B.

Now again as bob rises above ground to position C, K.E., decreases to zero and P.E. = mgh

∴ Sum of P.E. and K.E. = mgh

We see that in all three places, P.E. + K.E., i.e., the mechanical energy of the system, remains constant.