(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1. a force of 5 pounds compresses a 15-inch spring a total of 4 inches. how much work is done in compressing the spring 7 inches?

2. how much work is done in compressing the spring in exercise 1 from a length of 10 inches to a length of 6 inches?

2. Relevant equations

hooke's law: F=kd

3. The attempt at a solution

1.

F(k)=kx

5=k(4)

k=5/4

[tex]W = \int^7_0 (\frac{5}{4}x)dx[/tex]

[tex]\frac{5}{4}[\frac{1}{2}x^2]^7_0[/tex]

[tex]=\frac{245}{8} in-lb[/tex]

note: i know that the above is correct, but it is needed for the second question, which i am unsure of.

2.

[tex]W = \int\begin{array}{c} 10 \\ 6 \end{array}

(\frac{5}{4}x)dx[/tex]

[tex]\frac{5}{4}[\frac{1}{2}x^2]\begin{array}{c} 10 \\ 6 \end{array}[/tex]

[tex]\frac{5}{8}[x^2]\begin{array}{c} 10 \\ 6 \end{array}[/tex]

[tex]\frac{5}{8}[(10^2)-(6^2)]\begin{array}{c} 10 \\ 6 \end{array}[/tex]

[tex]=40 in-lb[/tex]

note: in the second problem, i couldn't figure out how to fix the intervals, but it is [6,10]. that is actually the part that i'm a little confused about. is that the right interval? do i use the same k from the first problem? thanks in advance to any who can help.

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# Homework Help: Work and spring problem

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