Question

Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest? What happens to its energy eventually? Is it a violation of the law of conservation of energy?

Answer 1

In the case of pendulum energy in the Bob at any instant of time, can be either potential energy (P.E) or kinetic energy (K.E) or a mixture of both but its total energy at any instant of time remains constant. This can be illustrated by below illustration in the figure.

In case of pendulum energy in the Bob at any instant of time when the pendulum Bob is at position B.It has only potential energy(P.E) and no kinetic energy(K.E).
As the Bob starts moving from position B to position A potential energy(P.E) decreases but Kinetic Energy(K.E) increases.
When the Bob reaches position A, there is only kinetic energy(K.e) but no potential energy(P.E).
As Bob moves from position A to position C, potential energy(p.E) increases but kinetic energy decreases.
When Bob reaches position C, Bob stops for a very small instant of time, At that time, Bob has only potential energy but no kinetic energy.
The Bob eventually comes to rest due to the frictional force offered by the air and the rigid support holding the thread.
It is not a violation of the law of conservation of energy since mechanical energy can get converted into another form of energy which cannot be utilized for useful work. This loss of energy is called dissipation of energy.