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?

1. Initial Energy States:
– Potential Energy: When the pendulum bob is drawn to one side, it gains potential energy due to its height above the equilibrium position.
– Kinetic Energy: Initially, the pendulum bob is at rest, so it possesses zero kinetic energy.

2. Conversion of Potential to Kinetic Energy:
– As the pendulum swings downward, potential energy converts into kinetic energy. At the lowest point of the swing, all potential energy is converted to kinetic energy.
– The pendulum reaches its maximum kinetic energy at the bottom of the swing, moving at its maximum speed.

3. Oscillation and Energy Transformation:
– The pendulum continues to oscillate, with energy continuously transforming between potential and kinetic forms as it swings back and forth.

4. Energy Dissipation:
– Factors like air resistance, friction at the pivot, and internal friction cause the pendulum to lose energy gradually.
– The lost energy transforms into less usable forms such as heat and sound, dissipating into the surroundings.

5. Decrease in Amplitude:
– As energy dissipates, the pendulum’s amplitude (maximum swing angle) decreases gradually with each swing.
– Eventually, due to energy losses, the pendulum comes to rest at its equilibrium position.

6. Conservation of Total Energy:
– While the pendulum eventually stops moving, the total energy of the system (including the pendulum and its surroundings) remains constant.
– Energy is not lost but rather transformed into less available forms, conforming to the law of conservation of energy.

7. Energy Transformation Summary:
– Initial potential energy is converted to kinetic energy during the swing.
– Energy dissipates due to various factors, leading to a decrease in motion until the pendulum eventually comes to rest.
– The total energy within the system and surroundings remains conserved, even though it becomes less available for useful work due to dissipation.