# Homework Help: Potential energy and work

1. Oct 10, 2012

### daivinhtran

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

What is the difference between "the work required to stretch a spring" and "the work done by a spring"?

2. Relevant equations

Fdx = dW
F (from the spring)= -kx
so, F (from me) = kx
3. The attempt at a solution
I have tried and I found out the work required to stretch a spring x1 to x2 is(1/2)k(x2^2 - x1^1)

and "the work dont by a spring" when it's released from x1 to x2 is the same thing but in opposite sign

Am I right?

2. Oct 10, 2012

### Staff: Mentor

Yes, except for the word "released". When you stretch the spring from x1 to x2, you do positive work on the spring--that's the work required to stretch the spring, which becomes spring potential energy. At the same time, as the spring is being stretched it is doing negative work on you.

3. Oct 10, 2012

### daivinhtran

Thank you
I meant "released" as in another situation.
If the spring is already compressed and then is released from x1 to x2
the work done by the spring is -(1/2)k(x2^2 - x1^1) (because the force is pointing in opposite direction.

I'm still confused when you say "that's the work required to stretch the spring, which becomes spring potential energy." By the definition the ΔU= - W(done by the spring) , not by me though

4. Oct 10, 2012

### daivinhtran

5. Oct 10, 2012

### Staff: Mentor

If it's compressed and being released, then x1 > x2. Right?
This is confusing, since I don't know if x1 > x2.

If W is the work done by the spring, then -W is the work done by you. If you stretch the spring, the spring does negative work. (Since force and displacement are opposite.) Thus you do positive work and ΔU is positive.

6. Oct 10, 2012

### daivinhtran

I finally got it...