# Finding x for a spring using energy equations

1. May 3, 2013

### cbasst

1. The problem statement, all variables and given/known data

This isn't a homework question, just something I've been thinking about. If given a situation in which mass m is hung on a spring with constant k, I know you can set the spring force equal to the weight of the mass to find how far it stretches. Is there a way to find how far it stretches using energy equations? It seems like it should be doable, but I can't figure out how.

2. Relevant equations

w = mg
F = -kx
ΔUg = mgh
Us = kx2/2

3. The attempt at a solution

As I said, setting mg = kx can solve for x. How do I do it with energy though?
Ug = Us
mgx = kx2/2

But now I get a different answer for x. What did I do wrong with the energy equations?

2. May 3, 2013

### Infrared

The energy approach will give you the farthest the mass on the spring will fall. This is not the equilibrium position. Think about it, if I let the mass drop, then when it passes the equilibrium position, it will not have zero velocity.

3. May 3, 2013

### cbasst

Ah. This makes sense now! Thanks!