Question

A force is given by Fx=Ax^-3, where A=8.0 N*m^3.(a) For positive values of x,does the potential energy associated with this force increase or decrease with increasing x?(You can determine the answer to this question by imagining what happens to a particle that is placed at rest at soke point x and is then released.) (b) Find the potential energy function U associated with this forse such that U approaches zero as x approaches infinity.

Answer 1

a) force= A/x^3 as x increases, it is positive, even though decreasing, it adds energy to a system.
b)

Potential energy= INT Fdx
= int Adx/x^3= -A/2x^2 +C
and apply the limits.