Calc-Force Problem: Work Done Stretching Spring 6 Inches

[J.live]

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.

 

[LawlQuals]

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.

 

[J.live]

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.

 

[J.live]

nobody? :/

 

[Dick]

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.

 

[J.live]

So..

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

 

[Dick]

So..

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

Yes.

 

[J.live]

Thank you.