Calculating Work on a Stretched Spring

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SUMMARY

The discussion centers on calculating the work done on a spring that follows the restoring force equation F = -kx + βx³, with k = 8.7 N/m and β = 95 N/m³. The user attempted to calculate the force at a stretch of 0.105 m, resulting in F = -1.02 N, and subsequently calculated work using W = F * d, yielding an incorrect result of -0.107 J. The consensus is that the problem lacks critical information regarding the proportional limit stretch distance, necessary for correctly applying the force equations.

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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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