What Differentiates Work Done by a Spring vs Work Required to Stretch It?

[daivinhtran]

Homework Statement

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

Homework Equations

Fdx = dW
F (from the spring)= -kx
so, F (from me) = kx

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 don't by a spring" when it's released from x1 to x2 is the same thing but in opposite sign

Am I right?

 

[Doc Al]

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 don't by a spring" when it's released from x1 to x2 is the same thing but in opposite sign

Am I right?

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.

 

[daivinhtran]

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.

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

 

[daivinhtran]

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.

Can you explain me please?

 

[Doc Al]

Thank you
I meant "released" as in another situation.
If the spring is already compressed and then is released from x1 to x2

If it's compressed and being released, then x1 > x2. Right?

the work done by the spring is -(1/2)k(x2^2 - x1^1) (because the force is pointing in opposite direction.

This is confusing, since I don't know if x1 > x2.

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

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.

 

[daivinhtran]

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.

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.

I finally got it...