Which statement about the work-energy relation is true when no net work is done on an object?

Which statement about the work-energy relation is true when no net work is done on an object?

• A. ΔK > 0.
• B. ΔK < 0.
• C. ΔK = 0.
• D. ΔK equals the change in potential energy.

Answer: (C)

The work-energy relation tells us that the net work done on an object equals the change in its kinetic energy. If no net work is done, then the change in kinetic energy must be zero, so the kinetic energy stays the same (the speed stays constant in the nonrelativistic case). Potential energy can change if energy is exchanged with other forms, but that does not force a change in kinetic energy when the total work sums to zero. So the correct statement is that ΔK is zero.

The work-energy relation tells us that the net work done on an object equals the change in its kinetic energy. If no net work is done, then the change in kinetic energy must be zero, so the kinetic energy stays the same (the speed stays constant in the nonrelativistic case). Potential energy can change if energy is exchanged with other forms, but that does not force a change in kinetic energy when the total work sums to zero. So the correct statement is that ΔK is zero.