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Chapter 7: Problem 6

If the force is zero at a given point, must the potential energy also be zero at that point? Give an example.

Short Answer

Expert verified
No, the potential energy doesn't have to be zero where the force is zero. An example is a pendulum at its highest point where the force is zero, but the potential energy is not, as it's raised above the lowest point of the swing.

Step by step solution

01

Understand The Relationships

Potential energy \( U \) and force \( F \) are not straightforwardly connected. Force is technically the negative derivative of the potential energy with respect to position: \( F = -\frac{dU}{dx} \). When the derivative is zero (force is zero), it implies that at that position, the potential energy \( U \) is at a minimum or maximum, not necessarily zero.
02

Example

Consider a pendulum at the highest point of its swing. The force gravity exerts on the pendulum is zero at this point, as it's neither pulling the pendulum up or down. However, the pendulum has potential energy because it's raised above the lowest point of the swing, and this energy will be converted to kinetic energy as the pendulum begins to swing back down.

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