Which statement correctly relates the gravitational potential energy change and the work done by gravity?

Which statement correctly relates the gravitational potential energy change and the work done by gravity?

• A. W_by_gravity increases gravitational potential energy
• B. delta U_grav is independent of height change
• C. delta U_grav = - W_by_gravity
• D. W_by_gravity = delta U_grav

Answer: (C)

The work done by gravity and the change in gravitational potential energy have opposite signs because gravity is a conservative force. If you raise an object by a height change ∆h, the gravitational potential energy increases by ∆U_grav = m g ∆h. When the object moves, gravity does work W_by_gravity = F_g · ∆r, which for vertical motion is - m g ∆h if you lift it upward (gravity acts downward while you move up), and + m g ∆h if it falls downward. The key relation is ∆U_grav = - W_by_gravity. So, the change in gravitational potential energy equals the negative of the work done by gravity. This explains why lifting up increases potential energy while gravity does negative work, and letting it fall decreases potential energy while gravity does positive work. The other statements conflict with this sign relationship and dependence on height change.

The work done by gravity and the change in gravitational potential energy have opposite signs because gravity is a conservative force. If you raise an object by a height change ∆h, the gravitational potential energy increases by ∆U_grav = m g ∆h. When the object moves, gravity does work W_by_gravity = F_g · ∆r, which for vertical motion is - m g ∆h if you lift it upward (gravity acts downward while you move up), and + m g ∆h if it falls downward. The key relation is ∆U_grav = - W_by_gravity.

So, the change in gravitational potential energy equals the negative of the work done by gravity. This explains why lifting up increases potential energy while gravity does negative work, and letting it fall decreases potential energy while gravity does positive work. The other statements conflict with this sign relationship and dependence on height change.