In a freely falling object, which statement best describes mechanical energy?

In a freely falling object, which statement best describes mechanical energy?

• A. Potential energy decreases as kinetic energy increases, and the total mechanical energy stays constant.
• B. Kinetic energy increases while potential energy remains zero.
• C. Total energy is not conserved because gravity adds energy.
• D. Potential energy increases as kinetic energy increases.

Answer: (A)

In free fall with gravity as the only force, mechanical energy is conserved. As the object drops, its gravitational potential energy (mgh) decreases because height h is smaller. At the same time, the speed increases, so its kinetic energy (1/2 mv^2) increases. The total mechanical energy, which is the sum of potential and kinetic energies, stays the same if we neglect air resistance: mgh + 1/2 mv^2 = constant. So the useful description is that potential energy decreases as kinetic energy increases, while the total mechanical energy remains constant. Gravity doesn’t add energy; it simply transfers energy between potential and kinetic forms. If air resistance were present, some energy would dissipate as heat, and the total mechanical energy wouldn’t be perfectly conserved, but in ideal free fall it is.

In free fall with gravity as the only force, mechanical energy is conserved. As the object drops, its gravitational potential energy (mgh) decreases because height h is smaller. At the same time, the speed increases, so its kinetic energy (1/2 mv^2) increases. The total mechanical energy, which is the sum of potential and kinetic energies, stays the same if we neglect air resistance: mgh + 1/2 mv^2 = constant. So the useful description is that potential energy decreases as kinetic energy increases, while the total mechanical energy remains constant. Gravity doesn’t add energy; it simply transfers energy between potential and kinetic forms. If air resistance were present, some energy would dissipate as heat, and the total mechanical energy wouldn’t be perfectly conserved, but in ideal free fall it is.