Question

(a) State and explain the law of conservation of energy with an example.
​(b) Explain how, the total energy a swinging pendulum at any instant of time remains conserved. Illustrate your answer with the help of a labelled diagram.

Answer 1

(a) The law of conservation of energy states that energy can neither be created nor be destroyed, but it can be transformed from one form to another. Example: When a body is thrown upward with some velocity, the total energy throughout the motion remains conserved. As the body moves upward, the kinetic energy of the body gradually gets converted into potential energy of the body and when the body falls back to the ground the potential energy of the body gets converted back into its kinetic energy and the body return back with the same velocity it was thrown upward.

(b)


A swinging pendulum is a perfect example to show the conservation of energy. The total energy of the bob of the pendulum is the sum of the potential energy and kinetic energy. Initially, the bob of the pendulum is at the mean position (B). When the bob is drawn to one side (Extreme position A), and raised to a little height, it gains some potential energy.

This is the energy transferred by work done by the hand. At the extreme position, the bob has only P.E. When it's left at the extreme position, it moves down. Then the P.E. decreases and K.E. increases. At the lowest (mean) position, the bob only has the K.E.

But as soon as it moves further to mean position, its K.E. decreases, and P.E. increases. At the extreme positions A and C, all energy is in the form of potential energy and therefore it tends to move down. At all other intermediate positions, the energy of the pendulum is partly potential and partly kinetic. But, the total energy of the pendulum remains conserved.