For a simple pendulum swinging back and forth, at which point does the pendulum have the greatest $kinetic energy$?

• A. Halfway between the lowest and highest points
• B. At all points, the $kinetic energy$ is the same
• C. At the highest points of its swing (the endpoints)
• D. At the lowest point of its swing (the equilibrium position)

Answer: (D)

Verified step by step guidance

1. Understand that a simple pendulum converts energy between potential energy (PE) and kinetic energy (KE) as it swings.
2. Recall that at the highest points of the swing (the endpoints), the pendulum momentarily stops, so its velocity is zero and kinetic energy is zero.
3. At the lowest point of the swing (the equilibrium position), the pendulum has its maximum speed because all the potential energy has been converted into kinetic energy.
4. Use the energy conservation principle: total mechanical energy E = PE + KE is constant, so when PE is minimum (at the lowest point), KE is maximum.
5. Therefore, the pendulum has the greatest kinetic energy at the lowest point of its swing, where its speed is highest.