Which of the following pairs correctly identifies an example of $\mathrm{kinetic} \mathrm{energy}$ and an example of $\mathrm{potential} \mathrm{energy}$ found in a typical home?

• A. A moving ceiling fan ($\mathrm{kinetic} \mathrm{energy}$) and a stretched rubber band ($\mathrm{potential} \mathrm{energy}$)
• B. A book lying on a table ($\mathrm{kinetic} \mathrm{energy}$) and a running faucet ($\mathrm{potential} \mathrm{energy}$)
• C. A refrigerator door closed ($\mathrm{kinetic} \mathrm{energy}$) and a rolling ball ($\mathrm{potential} \mathrm{energy}$)
• D. A turned-off television ($\mathrm{kinetic} \mathrm{energy}$) and a swinging pendulum at its lowest point ($\mathrm{potential} \mathrm{energy}$)

Answer: (A)

Verified step by step guidance

1. Recall that kinetic energy is the energy an object possesses due to its motion. Mathematically, kinetic energy is given by \(E_k = \frac{1}{2} m v^2\), where \(m\) is mass and \(v\) is velocity.
2. Potential energy is the energy stored in an object due to its position or configuration. For example, elastic potential energy in a stretched rubber band or gravitational potential energy in an elevated object.
3. Analyze each pair by identifying which object is moving (kinetic energy) and which object is storing energy due to position or deformation (potential energy).
4. For example, a moving ceiling fan is clearly in motion, so it has kinetic energy. A stretched rubber band is deformed and stores elastic potential energy.
5. Compare the other options and note that objects at rest or turned off do not have kinetic energy, and running water or a rolling ball in motion have kinetic rather than potential energy.