Given a potential energy function U(x), the corresponding force is in the positive x direction if:
A)U is positive
B)U is negative
C)U is an increasing function of x
D)U is a decreasing function of x
E)it is impossible to obtain the direction of from U

Question

Given a potential energy function U(x), the corresponding force  is in the positive x direction if:
A)U is positive 
B)U is negative 
C)U is an increasing function of x 
D)U is a decreasing function of x 
E)it is impossible to obtain the direction of from U

Quizplus · Accepted Answer

The force is given by the gradient of the potential energy function, so:

11eab079_96ce_5f9f_a51f_1bea3323afdc_TB6585_11 = -dU/dx

If U is decreasing with increasing x, that means dU/dx is negative, so the force is positive in the x direction. Therefore, the correct choice is D, U is a decreasing function of x.

Given a Potential Energy Function U(x), the Corresponding Force