k isn't right. Look at how the problem is worded.
Here is the quesiton:
A spring has a natural length of 2 feet. If a force of 6 lbs is needed to maintain a compression of 6 in., how much work is needed to compress the string from natural length to a length of 16 in.? Round to 4 decimal places.
I'm almost positive I'm solving this correctly but it is wrong according to my online quiz.
F(x) = k * x where k is spring constant and x is distance compressed from natural length.
-6 lb = k * -18 in (Natural length of 2 ft = 24 inches. 24 - 6 in = 18. Negative for compression.)
k = 1/3 lb/in
F(x) = k* x = 1/3x
Integral from 8 to 0 (24 in - 16 in = 8 in) of 1/3x gives me a work value of 10.6667. However this is not the correct answer apparently. I don't understand what I'm doing wrong. I also tried it with converting everything to feet instead of inches and got 3.5556 for final answer, but that is not correct either.
What am I doing wrong? Any help is greatly appreciated
No. The spring is "centered" at 24 inches. Let x = how far the spring is compressed from that, NOT the distance that the spring is compressed from the 0-inch mark.
So if it's compressed 6 inches, F = 6 as well, giving you your k.