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

A mass, m, is dropped from a height, h, on an initially uncompressed spring of length L.

(a) Determine the amount by which the spring is compressed before the mass comes to rest.

(b) Determine the mass's maximum speed.

2. Relevant equations

U(e)=.5k*x^2, U(g)=mgh, KE=.5mv^2

I think I am supposed to do this all symbolically, since I don't have k.

3. The attempt at a solution

For part (a):

So, take the bottom of compression to be the 0 for gravitational potential energy. Then, we can say that the mass is dropped from a distance d above the top of the unstretched spring, where d=h-L. If the spring compresses by a distance, x, then let us call L-x the 0 for gravitational potential energy. I end up with this conservation of energy equation:

E0=Ef... so: mg(h)= .5k*x^2+ mg(L-x)

This simplifies to: 0=.5k*x^2-mgx-mg(L-h)

I can use the quadratic equation to solve this, but is that too complicated for this type of question? Which solution to that equation would I use, the + or the - section?

For part (b), I believe I find the new equilibrium position of the mass (x=mg/k) and then plug that into the conservation of energy as the x, solving for v at that point. Correct?

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# Mass Dropped on Vertical Spring

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