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? A) The force on the two systems will be in opposite directions. B) The force is identical on the two systems. C) The force on the second system will be with less than the force on the first system. D) There is no relationship between the forces on the two systems. E) The force on the second system will be with greater than the force on the first system.

Question

Quizplus · Accepted Answer

The force on each system is dependent solely on its potential energy function's derivative with respect to x. Since U1(x) and U2(x) both have the same x-dependent terms (Cx² and Bx³), the force on each system will be identical for a given position. The quantity A in U2(x) does not affect the x-dependence of the potential energy function and therefore does not affect the force.

A Potential Energy Function for System 1 Is Given by U1(x)