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.
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.
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?