Extremely Confusing Energy Question - Involves Springs

[Foon]

I drew out a diagram for this question and wrote out all my givens. I looked through all the formula's I have and I just can't put the pieces of the puzzle together. If anyone can help that would be greatly appreciated.

Question:

A 1.5kg steel mass is dropped onto a vertical compression spring of force constant 2.1 x 10^2 N/m, from a height of 0.37m above the top of the spring. Find, from energy considerations, the maximum distance the spring is compressed.

Thanks!

 

[chroot]

Work is the integral of force over distance.

The spring applies a force equal to F = kx. The work done in compression is the integral of that force over distance:

W = integral (from 0 to p) (k x dx)
= 1/2 k x^2 | p
= 1/2 k p^2

where p is the maximum compression distance.

Find the gravitational potential energy released by a 1.5 kg mass moving 0.37m downwards (it's just [delta]E = m g y). Set it equal to the work done in the spring's compression, and solve for p.

- Warren

 

[Chi Meson]

I'm guessing that this is not a calculus-based class, is it?

Without calculus it's the same as Chroot said, but it looks a little different. Use conservation of energy, the gravitational potential energy at height "h" above the spring equals the total elastic potential energy of the spring when compressed a distance "x." The trick here is that the distance the mass falls is "h+x." THis is going to lead you to a quadratic solution.
mg(h+x) = 1/2 kx^2.