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 ?\

Explanation

Let us consider a pendulum suspended from the point S as shown in fig. 5.19 (i) When we drew the pendulum to one side (say B), it rises through a height , h and its potential energy, `E_p` = mgh and kineitc energy,`E_k = 0` (as it is at rst at B.)
(ii) As it moves from B to O, its velocity increases and its `E_p` gets converted into `E_k` At the point O, it has maximum velocity and as such maximum `E_k` whereas `E_p = 0`
(iii) When it moves from O to A, its velocity decreases but at the same time, it is raised up through a height. As such it gains `E_p.` At A, where it temporarily comes to rest, its has maximum value of `E_k into E_p.` Thus, When the pendulum oscillates between the extremes A and B there is continous exchange between `E_p and E_k` and the sum total of the two types of energy `(E_p and E_k)` remains constant, according to law of conservation of energy. This is true in case there is no loss of energy due to external factors.

The bob eventually comes to rest as it loses energy due to : (i) air resistance offered to the bob and (ii) the friction at the point of support, S. The energy of the bob is : (i) gained by the air molecules which gain speed as the bob strickes them and (ii) used up in prodcuing heat and sound at the point of support. The entire process is according to the law of conservation of energy where energy only changes from one from to the other.