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Question

(a) State and explain the law of conservation of energy with an example.

(b) Explain how the total energy of a swinging pendulum at any instant of time is conserved. Illustrate your answer with the help of a labelled diagram.

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Solution

(a) The law of conservation of energy implies that energy can neither be created nor destroyed, but can be changed from one form to another. The law of conservation of mass states that the total amount of mass remains constant in an isolated system in spite of any physical or chemical changes that may take place.

The law of conservation of energy can be seen in these everyday examples of energy transference:

  • Water can produce electricity. Water falls from the sky, converting potential energy into kinetic energy. This energy is then used to rotate the turbine of a generator to produce electricity. In this process, the potential energy of water in a dam can be turned into kinetic energy which can then become electric energy.
  • When playing pool, the cue ball is shot at a stationary 8 ball. The cue ball has energy. When the cue ball hits the 8 balls, the energy transfers from the cue ball to the 8 ball, sending the 8 balls into motion. The cue ball loses energy because the energy it had has been transferred to the 8 balls, so the cue ball slows down.
  • Kelly ran across the room and bumped into her brother, pushing him to the floor. The kinetic energy she possessed because of her movement was transferred to her brother, causing him to move

(b) A swinging simple pendulum is an example of conservation of energy :
This is because a swinging simple pendulum is a body whose energy can either be potential or kinetic or a mixture of potential and kinetic, but its total energy at any instant of time remains the same.

When the pendulum bob is at position B, it has only potential energy (but no kinetic energy).
As the bob starts moving down from position B to position A, its potential energy goes on decreasing but its kinetic energy goes on increasing.
When the bob reaches the centre position A, it has only kinetic energy (but no potential energy).
As the bob goes from position A towards position C, its kinetic energy goes on decreasing but its potential energy goes on increasing.
On reaching extreme position C, the bob stops for a very small instant of time. So at position C, the bob has only potential energy (but no kinetic energy).



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