Question

A force of 8 lbs. is needed to compress a spring 2 inches. Find the work done compressing the spring from its natural length of 18 inches to the length of 12 inches.

Answer 1

There are actually two problems here: finding the spring constant and then using that to find the work done. Hooke's Law is given by:\[F=-kx\]where F is the force; k is the spring constant; and x is the amount the spring is compressed (or stretched) from its natural length. You can use the information given in your problem along with Hooke's Law to find the spring constant.

Answer 2

Once you've got the spring constant you're ready to find the work done compressing your spring. The energy stored in a spring is given by:\[E _{spring}=\frac{ 1 }{ 2 }kx ^{2}\]The only way to store energy in a spring is to do work on that spring, therefore:\[W=E _{spring}\]

Answer 3

Does that help?

Answer 4

F= kx
8 = k(4)
8/4 = k
4 = k

Answer 5

I think you meant to type a '2' instead of a '4' for x, but you are otherwise correct that k=4 lbs/in.

Answer 6

\[W=\int\limits_{a}^{b}F_xdx=\int\limits_{2}^{6}(4x)dx\]

Answer 7

ya it's d = 2 I typed it wrong. so k= 4x

Answer 8

is my limit correct?

Answer 9

Yes, the integral you set-up is correct. Note that the formula I gave for Energy/Work is just the indefinite integral of Hooke's Law with respect to x.

Answer 10

yeah. I see that since it is already an integrated value (x^2)/2

Answer 11

thank you

Answer 12

You're welcome.