Question

A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces potential energy U(x) given by U(x) = αx4 , where α = 1.25 J/m4. What is the force (magnitude and direction) when the particle is at x = -0.856 m?

Answer 1

here ,

potential energy , U(x) = 1.25 * x^4 J

Now, as the force is given as

Fx = -dU/dx

Fx = -d/dx(1.25 * x^4)

Fx = - 5 x^3

for x = -0.856 m

Fx = -5 * (-0.856)^2

Fx = 3.136 N

the force acting on the particle in x -direction is 3.136 N in +ve x-direction