# How much work must you do to change length of spring?

#### enchanteuse

1. Homework Statement
A spring has a relaxed length of 7 cm and a stiffness of 200 N/m. How much work must you do to change its length from 10 cm to 14 cm?

2. Homework Equations
Ef = Ei + W

3. The Attempt at a Solution
Ef = Ei + W
Ef = Ei + F*delta x
F*delta x = Ef - Ei
F*delta x = (Ki + Ui) - (Kf + Uf)
F*delta x = (1/2mvi^2 + 1/2ks si^2) - (1/2mvf^2 + 1/2ks sf^2)

I'm trying to break this equation apart to try to figure this out, but I'm not sure what to do next. Help!

Thanks

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#### LowlyPion

Homework Helper
You're making things too hard.

W = ∫ F*X dx

And what is F?

F = -k*x

so ...

#### Sumanyu

Thinking about Hooke's Law

Since,

Force = -k * delta x

Force = 200N/m * 14 - 10 cm

or

Force = 200N/m * 0.04m

= Force required = 8N

Work = Force x Distance

Work = 8N x .04m

= 0.32 J

#### enchanteuse

Wouldn't it be -0.32 J since F = -k * delta x?

#### Sumanyu

Wouldn't it be -0.32 J since F = -k * delta x?
Sure =)

I ignored the -...

#### enchanteuse

Hmm well the answer supposedly isn't 0.32 J or -0.32 J.

The way you answered it makes perfect sense though...

I think you need to incorporate the 7 cm, but I'm not sure how.

#### LowlyPion

Homework Helper
Hmm well the answer supposedly isn't 0.32 J or -0.32 J.

The way you answered it makes perfect sense though...

I think you need to incorporate the 7 cm, but I'm not sure how.
The limits of your integration are from .10 - .07 = .03 to .14 - 07 = .07.

-1/2k*x2 = 1/2*200*(-.032 + .072)

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