1. The problem statement, all variables and given/known data You decide the spring constant k of a spring by measuring the extension x at different loads. Result is displayed in diagram: 4 cm extension = 10 newton 4.5 cm extension = 11 newton 6 cm extension = 15 newton The graph which I have is uploaded here: http://nces.ed.gov/nceskids/createagraph/index.asp?ID=5881274468fc4a8e9f509058747271cb (Just press preview) a) Determine the spring constant. b) How much work does it take to extend the spring by 4.5 cm? 2. Relevant equations k = N/d (d = distance) W = F * d 3. The attempt at a solution a) Ok, so I start out with deciding the spring constant. I know 4 cm is 10 newton, so I begin: k = 10 N / 0.04 m k = 250 N b) Then I try to figure out the work: I see that the spring at 4.5 centimeters takes 11 newton of force. W = 0.045 * 11 W = 0.0495 J However the solution says it's 0.25 J. My teacher tried to explain it has to do with the average length, that because of this you have to divide your work in 2. So: W = (0.045*11)/2 W = 0.2475 J and rounded: 0.25 J Also he tried to explain that I could use the spring constant equation: k = F/d k * d = (F/d)*d k * d * d = F * d k * d^2 = F * d <- Where I see the point that this is also work. But still, why do I have to divide the given work in two? Thanks for any help.