Solve the Work-Energy Problem: Is There a Mistake?

Thread starter eurekameh
Start date Apr 19, 2012
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Work-energy

AI Thread Summary

The discussion centers on the calculation of work done by a spring, with a focus on whether the initial answer provided is incorrect. The potential energy of a spring is correctly stated as U = (1/2) k x^2. The work done by the spring is derived from the spring force equation, leading to the same result: W = (1/2) k x^2. There is a consensus that the calculations align correctly with the principles of physics. The thread concludes that the initial understanding of the work-energy problem is accurate.

Apr 19, 2012

eurekameh

Is this answer wrong? I think they've made a mistake in the work done by the spring, which I think should be (1/2)(135)(0.5)^3?

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Apr 19, 2012

Steely Dan

No, the potential energy of a spring is indeed U = \frac{1}{2} k x^2. If you want to think of it as work, then know that the spring force is F = k x, so the work done is
W = \int F dx = \int k x dx= \frac{1}{2} k x^2,
which is the same answer.

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