A spring of length D and constant k is hung from the ceiling. A nonstretchable string of length L is attached to the bottom of the spring. An object of mass m attached to the free end of the string and dropped from the ceiling. What is the lowest the object would reach?(adsbygoogle = window.adsbygoogle || []).push({});

I'm supposed to solve this strictly using energy. No amplitude or anything like that.

Here I go:

E = Ug + Us

Ug = (D + L)mg

Us = .5kx^{2}

That all I know about U. How do I find how far the spring stretches past its equilibrium position, when it stretches the farthest away from the point of origin?

This is my guess:

Since it's all potential energy at the time of release, the spring is unstretched:

mg(D + L) = .5kx^{2}

x = sqrt((2*mg(D + L))/k)

So the lowest point would be D + L + x

So can someone explain to me all the conceptual errors I made and how those concepts are supposed to apply in this situation? Thanks.

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# Homework Help: Cons. of energy problem

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