Question

Analyze the motion of a simple swinging pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfather clock has to be wound up.

Short answer

1. Mechanical energy will be conserved; the pendulum will reach the same height in each oscillation.
2. The pendulum will lose mechanical energy due to friction. The pendulum will reach less height in each successive oscillation.

Step-by-step solution

Grandfather clock

The grandfather clock is weight-driven. In this clock, the motion of the gears is achieved by the swing of the pendulum.

When there is no friction

As there is no friction, mechanical energy during the motion of the pendulum will be conserved. Thus, the pendulum will reach the same height in each oscillation.

When there is friction

When friction is present, mechanical energy will be lost due to friction, and the pendulum will reach less height in each successive oscillation, and that is why the Grandfather clock needs to be wound up.