(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Is the work done BY a spring always negative when you compress or stretch it?

2. Relevant equations

W=-1/2kx^2

3. The attempt at a solution

I know that the spring force always acts opposite of displacement when compressing or stretch. So when you compress or stretch the spring, the work the spring does should be -1/2kx^2. I'm having a hard time convincing myself mathematically though. So you compress the spring from x initial=0 m to a x final equal to some -4 m. The spring force according to this convention, F=-kx becomes a positive kx because the displacement is negative. When I integrate the force, do I put a a positive sign now, so in this case I would integrate the spring force from -4m to 0m? Also I know work is the Magnitude of the force times the Magnitude of the displacement for a constant force. Does this hold in varying forces such as the spring force?

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# Homework Help: Work done by Spring

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