Question

The potential energy U as a function of the position x of an object is given by U (x) = - 400/x, where U is in joules and x is in meters. The object is released from rest at position x = 30 m and is free to move along the x-axis. When the object has moved a distance of 10 m from its initial position, the magnitude of the force associated with this potential energy function is

Answer 1

Hi there!

We know that:

F = -dU/dx, so:

U = -400/x

dU/dx = 400/x² (Take the derivative)

F = -dU/dx = -400/x²

Finding the force at 10m away from the starting point (30m), means a position of 40m. So:

F = -400/(40²) = -0.25 N