Work by the spring equals negative change in potential energy. If the potential energy increases during the displacement, the work done by the spring is:

Work by the spring equals negative change in potential energy. If the potential energy increases during the displacement, the work done by the spring is:

• A. Positive
• B. Zero
• C. Negative
• D. It depends on velocity

Answer: (C)

The work done by a spring is tied to how its potential energy changes: W_spring = -ΔU. If the displacement causes the spring’s potential energy to increase, then ΔU > 0, so W_spring is negative. That means the spring is taking energy from the moving object rather than giving energy to it—the force from the spring opposes the motion, resulting in negative work. The sign of this work comes from the change in potential energy, not the speed of the object. When the spring’s energy increases, it stores energy (negative work on the object); when the spring’s energy decreases, it can do positive work on the object.

The work done by a spring is tied to how its potential energy changes: W_spring = -ΔU. If the displacement causes the spring’s potential energy to increase, then ΔU > 0, so W_spring is negative. That means the spring is taking energy from the moving object rather than giving energy to it—the force from the spring opposes the motion, resulting in negative work. The sign of this work comes from the change in potential energy, not the speed of the object. When the spring’s energy increases, it stores energy (negative work on the object); when the spring’s energy decreases, it can do positive work on the object.