Name: Law of Conservation of Energy
Uploaded: 2019-07-19
Duration: 8 min 56 s
Description: You put fuel into the tank of your car. Once you start your car, it moves forward. Did you realise that you converted chemical energy in the fuel to kinetic...

Question

Explain how, the total energy of a swinging pendulum at any instant of time remains conserved. Illustrate your answer with the help of a labelled diagram.

Accepted Answer

A simple pendulum consists of a small metal ball (called bob) suspended by a long thread from rigid support, such that bob is free to swing back and forth when displaced. Initially, the pendulum is at rest at centre position A (Refer image). The bob is pulled to one side to position B to give it potential energy and then released. The bob starts swinging forth and back. (i) When the bob is in position B, it has potential energy but no kinetic energy.

(ii) As the bob starts moving down from position B to A, its potential energy starts decreasing, and kinetic energy starts increasing.
(iii) When the bob is at position A, it has maximum kinetic energy and zero potential energy.
(iv) As the bob starts moving up from position A to C, its kinetic energy starts decreasing, and potential energy starts increasing.
(v) On reaching the extreme position C, the bob stops for a very small instant of time, and here the bob has maximum potential energy and zero kinetic energy.

Therefore, at extreme positions, B and C bob has only potential energy, and at A, it has only kinetic energy. At other intermediate positions, bob has both kinetic and potential energies. Thus, the total mechanical energy of the pendulum is constant for any instant of time (conserved).

Explain how, the total energy of a swinging pendulum at any instant of time remains conserved. Illustrate your answer with the help of a labelled diagram.

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