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

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Homework Help Overview

The problem involves calculating the work required to change the length of a spring from 10 cm to 14 cm, given its relaxed length of 7 cm and stiffness of 200 N/m. The discussion centers around the application of Hooke's Law and the work-energy principle.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between force and displacement in the context of Hooke's Law. There are attempts to derive the work done using integration and force calculations. Some participants question the signs of the work and force values, while others suggest incorporating the relaxed length of the spring into the calculations.

Discussion Status

The discussion is ongoing, with various interpretations being explored regarding the calculation of work. Some participants have provided guidance on using integration and the force equation, while others express uncertainty about the correct approach and the incorporation of the relaxed length.

Contextual Notes

Participants note potential missing information regarding the expected answer and the implications of the spring's relaxed length in the calculations. There is a recognition of differing opinions on the sign of the work done.

enchanteuse
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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?

Homework Equations


Ef = Ei + W

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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You're making things too hard.

W = ∫ F*X dx

And what is F?

F = -k*x

so ...
 
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
 
Wouldn't it be -0.32 J since F = -k * delta x?
 
enchanteuse said:
Wouldn't it be -0.32 J since F = -k * delta x?

Sure =)


I ignored the -...
 
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.
 
enchanteuse said:
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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