Which statement best describes the relationship between the $\mathrm{potential energy}$ and $\mathrm{kinetic energy}$ of an object in a closed system?

• A. $\mathrm{Potential energy}$ and $\mathrm{kinetic energy}$ are unrelated and change independently of each other.
• B. As the $\mathrm{potential energy}$ of an object decreases, its $\mathrm{kinetic energy}$ increases, keeping the $\mathrm{total mechanical energy}$ constant.
• C. $\mathrm{Kinetic energy}$ is always greater than $\mathrm{potential energy}$ for any moving object.
• D. $\mathrm{Potential energy}$ and $\mathrm{kinetic energy}$ always increase together in a closed system.

Answer: (B)

Verified step by step guidance

1. Understand that in a closed system, the total mechanical energy is conserved, meaning the sum of potential energy (PE) and kinetic energy (KE) remains constant over time.
2. Recall the principle of conservation of mechanical energy, which can be expressed as: \(\text{Total Mechanical Energy} = PE + KE = \text{constant}\).
3. Recognize that when an object’s potential energy decreases (for example, when it falls), its kinetic energy increases by the same amount, so the total energy stays the same.
4. This inverse relationship means that potential energy and kinetic energy are interdependent and transform into each other, rather than changing independently or both increasing simultaneously.
5. Therefore, the best description is: as the potential energy of an object decreases, its kinetic energy increases, keeping the total mechanical energy constant.