A force parallel to the x-axis acts on a particle moving along the x-axis. The force produces a potential energy U (x) given by U (x) = ↵x4, where ↵ = 0.630 J/m4. What is the force (magnitude and direction) when the particle is at x = 0.800 m?

The force acting on the particle at x = -0.800 has magnitude of 1.29 N and directed toward the origin

Explanation:

First we write the potential energy produced by the force

where α = 0.630

therefore

For motion along a straight line, a conservative force is the negative derivative of its associated potential energy function U(x):

therefore

At  x = -0.80 the force equals

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