Force and potential energy: A potential energy function for system 1 is given by U₁(x) = Cx² + Bx³. The potential energy function for system 2 is given by U₂(x) = A + Cx² + Bx³, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position?

Question

Quizplus · Accepted Answer

The force on a system is given by the negative gradient of its potential energy function. Since the potential energy functions of system 1 and system 2 have the same coefficients for x, the negative gradients of the two functions will also be identical, i.e., the force is identical on the two systems.

Force and Potential Energy: a Potential Energy Function for System