Calculating Work on a Stretched Spring

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The discussion revolves around calculating the work done on a spring stretched beyond its proportional limit, using the equation F=-kx+βx³. The user initially calculates the force as -1.02 N but realizes that their work calculation yields an incorrect result of -0.107 J. They express confusion over the need for the stretch distance of the proportional limit to determine when to switch formulas. Other participants agree that the problem lacks crucial information regarding the proportional limit. The conversation highlights the importance of understanding the transition between linear and nonlinear spring behavior in calculations.
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Homework Statement


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.


Homework Equations


W= F*d


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!
 
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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.
 
Delphi51 said:
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.
That sounds logical to me. The problem is missing one vital piece of information.

shrutij, what is the given correct answer?
 

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