# Conservation of energy springs.

1. Dec 6, 2005

### computer_geek

Hello, I have a question regarding the conservation of energy.

So you have a long spring (the kind that wants to stay closed, as in when you pull on it, it reacts in the opposite direction) situated in a vertical position. You attach the weight to the bottom of the spring, and let it bounce up and down several times.

Now, using distance sensors and what not, you can calculate kinetic, potential (gravitational), and potential (elastic) energy. Would it be correct to assume that when the 3 are added together, a somewhat constant value is achieved?

Well, that's what my teacher claims. I think otherwise because although (potential) gravitational energy decreases when (potential) elastic energy increases, they change at different rates, therefore not resulting in a straight line when added.

Any comments would be greatly appreciated!
Thanks

2. Dec 6, 2005

### physicsfox

Why do you think the PEspring and PEgrav change at different rates? Think about this question: If an object falls from rest, from a height of h, the object has PE defined by mgh, and KE defined by 1/2mv^2. These also appear to change at different rates... yet you would probably agree that as the PE decreases, the KE increases by the exact same amount. The spring system is, in a way, very similar. Back to the freefall example - try sketching graphs of PE vs. time, and on the same axis, KE vs. time. (As a start, also think about your Vel. vs. time graph for an object in freefall - your KE graph would be the square of the Vel. vs. time)