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