A pendulum bob swings from point B to point C along the...

A pendulum bob swings from point B to point $C$ along the circular arc indicated in Figure 6.10. (a) Is the work done on the bob by gravity positive, negative, or zero? Explain. (b) Is the work done on the bob by the string positive, negative, or zero? Explain.

Key Concepts

Work

Work is defined as the dot product of force and displacement. It quantifies the energy transfer to or from an object; if the force has a component in the direction of the displacement, work is done on the object. The sign of the work (positive or negative) depends on whether the force component is in the same or opposite direction relative to the displacement.

Conservative Forces

Conservative forces are those for which the work done is independent of the path taken and depends only on the initial and final positions. Gravity is an example of a conservative force, meaning the change in gravitational potential energy between two points is equal to the negative of the work done by gravity.

Centripetal Forces

Centripetal forces are always directed towards the center of the circular path and are perpendicular to the object's instantaneous tangent displacement. Since work is calculated by the dot product of force and displacement, any force that is perpendicular to the displacement does no work, regardless of the magnitude of the force.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. When an object moves between heights, the change in this potential energy is directly related to the work done by gravity, reinforcing the idea that the work done by gravity is equal to the negative change in gravitational potential energy.

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