What component of the gravitational force affects the pendulum's motion and does work?

The gravitational force acting on a pendulum has both horizontal and vertical components, but it is the vertical component that directly affects the pendulum's motion and does work.

As the pendulum swings, gravity exerts a force pulling it downward. This vertical component of the gravitational force is what causes the pendulum to accelerate downward, increasing its kinetic energy as it swings through its lowest point. When the pendulum is at the peak of its swing, the vertical component has the potential to convert gravitational potential energy into kinetic energy, allowing the pendulum to gain speed. The horizontal component, on the other hand, does not perform work on the pendulum since it does not contribute to the movement in the vertical direction, which is necessary for the change in potential energy.

Thus, the vertical component of the gravitational force is the key factor in driving the motion of the pendulum and enabling it to convert energy between kinetic and potential forms as it oscillates.