# Restoring Force

1. Feb 28, 2012

### shrutij

1. The problem statement, all variables and given/known data
When a certain spring is stretched beyond its proportional limit, the restoring force satisfies the equation F=-kx+βx3. If k=8.7 N/m and β=95 N/m3, calculate the work done by this force when the spring is stretched 0.105 m.

2. Relevant equations
W= F*d

3. The attempt at a solution
I found F by plugging in the values of k, β and x=0.105 m to get -1.02. The negative for the force value makes sense here since it is a restoring force acting in the negative direction. Am i wrong in this reasoning?
My answer is wrong, though since when I try W=F*d; =-1.02*.105, I get -0.107 J, which is wrong. Help!

2. Feb 28, 2012

### Delphi51

I am not an expert on this, but surely the formula is F = -kx for x between 0 and the proportional limit, then the more complex formula beyond that.
And you can't do the problem without knowing the stretch distance of the proportional limit so you know where to switch formulas.

3. Feb 28, 2012

### Staff: Mentor

That sounds logical to me. The problem is missing one vital piece of information.

shrutij, what is the given correct answer?