Calc-Force Problem: Work Done Stretching Spring 6 Inches

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Homework Help Overview

The problem involves calculating the work done in stretching a spring an additional 6 inches from an already extended length, given a specific force required to stretch it initially. The subject area is calculus, specifically focusing on integration and the application of Hooke's Law.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the setup for calculating work done, particularly focusing on the limits of integration and the spring constant. There are questions about whether to use limits from 3 to 9 inches or from 43 to 49 inches.

Discussion Status

The discussion is ongoing, with some participants clarifying their understanding of the spring constant and its implications for setting up the work calculation. There is a mix of attempts to resolve the limits of integration and some expressions of uncertainty about the correct approach.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can provide or the methods they can use. There is an emphasis on understanding the relationship between force, spring constant, and the limits for integration.

J.live
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Homework Statement



A Force of 7 pounds is required to stretch a 40 inch spring to a length of 43 inches. How much work will be done in stretching the spring an additional 6 inches from its already extended length of 43 inches?

The Attempt at a Solution



I know how to integrate , just having problems with taking limits.Will I take the limit from 3 to 9 inches or is it 43 to 49 inches? Will be great if someone can clear it out by explaining why. Thank you.
 
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On second thought (this is edited), I will assume you understand how to find the spring constant k and just were confused about the limits, which I should have done in the first place since that is what you asked.

Can you clarify how you are setting up your expression for calculating the work done? The limits of integration have all to do on just how you *choose* to write the spring force equation, nothing else.
 
Yes i Have calculated the spring constant which is

F(x)= k*x

F(9) = 7k

k= 9/7

Where I get stuck is taking limits for k.
 
nobody? :/
 
In the spring constant equation F(x)=k*x, x is the difference between the stretched length of the spring and the unstretched length of the spring. Try and compute k again. You know F(3)=7.
 
So..

K= 7/3. Then I take limit from 3 to 9 inches?
 
J.live said:
So..

K= 7/3. Then I take limit from 3 to 9 inches?

Yes.
 
Thank you.
 

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