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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, potential energy at a point does not have to be zero if the force is zero at that point. An example is a book resting on a table where there is no net force but the book has gravitational potential energy due to its position above the ground.

Step by step solution

01

Understand the concept of Force

Force is a vector quantity that refers to the interaction between two objects that changes (or tries to change) the state of motion of the objects. It can be zero if there is no interaction or if the interactions cancel each other out.
02

Understand the concept of Potential Energy

Potential energy is the energy that an object possesses due to its position in a force field or that a system has due to its configuration. It does not depend on the presence of a force but the relative positions of the objects.
03

Relation between Force and Potential Energy

The relationship between force and potential energy is given by the derivative of the potential energy with respect to position, \( -\frac{dU}{dx} \). If the derivative is zero, it means that the potential energy is not changing, and this does not necessarily mean that potential energy itself is zero. Hence, it is entirely possible to have zero force but non-zero potential energy.
04

Example

Consider a book placed on a table. There is no net force acting on the book (gravity and normal force from the table cancel each other out) but the book possesses gravitational potential energy due to its position above the ground. Hence, this is an example where the force is zero but the potential energy is not.

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