I have an assignment with the following problems...
The natural length of a certain spring is 16 inches and a force of 8 pounds is required to keep it stretched 8 inches. Find the work done in each case.
(a) stretching it from a length of 18 inches to a length of 24 inches.
First, I'll find the K constant and also convert from inches to feet to make my life easier.
If it's being extended 8 inches it's natural length, that should be 2/3 foot its natural length.
Here's the part where I'm slightly confused. I solved for K using two different methods and I'm getting two different answers
k • (2/3) = 8lb
k = = 12 ft.
However, using this method I get the following.
8 = =
8 = = 36
I did solve this problem using 36 and obtained 15/2, but now I'm not sure if this was the correct method.
(b) Compressing it from its natural length to a length of 12 inches
Regarding this compression problem, I'm also a bit confused since my assignment didn't show a compressing example. I'm assuming the integral would look something like =