How are $\mathrm{potential energy}$ and $\mathrm{kinetic energy}$ related in a closed system?

• A. $\mathrm{Potential energy}$ can be converted into $\mathrm{kinetic energy}$ and vice versa, conserving the total $\mathrm{mechanical energy}$.
• B. $\mathrm{Kinetic energy}$ can be converted into $\mathrm{potential energy}$, but $\mathrm{potential energy}$ cannot be converted into $\mathrm{kinetic energy}$.
• C. $\mathrm{Potential energy}$ and $\mathrm{kinetic energy}$ are unrelated and cannot be converted into each other.
• D. $\mathrm{Potential energy}$ is always greater than $\mathrm{kinetic energy}$ in a closed system.

Answer: (A)

Verified step by step guidance

1. In a closed system, the principle of conservation of mechanical energy states that the total mechanical energy (sum of potential energy and kinetic energy) remains constant if only conservative forces are acting.
2. Potential energy is the energy stored in an object due to its position or configuration. For example, gravitational potential energy depends on the height of an object above the ground.
3. Kinetic energy is the energy of an object due to its motion. It depends on the mass and velocity of the object.
4. In a closed system, potential energy can be converted into kinetic energy and vice versa. For example, when an object falls, its gravitational potential energy decreases while its kinetic energy increases, keeping the total energy constant.
5. The correct relationship in a closed system is that potential energy can be converted into kinetic energy and vice versa, conserving the total mechanical energy. This means that the total energy remains constant, but the forms of energy can change.