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Originally Posted by sanddrag
2 Joules of work is needed to stretch a spring from its natural length of 30cm to a length of 42 centimeters. How much work is needed to stretch it from 35cm to 40cm?
Sorry, I know this is simple but I'm messing up somewhere because I'm not getting the correct answer of 25/24 or approx. 1.04 Joules
Any help is appreciated. Thanks. 
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F = a x (where x is the "stretch" of the spring)
W is the integral of F, from 0 to the "stretch" of the spring
W = (a x^2) / 2
For a stretch of (42-30) you have that the work is 2 joules
Solve this for a, you now have the formula for work as
function of stretch of the spring. (a=4/144 in this case)
At this point, you subtract the work for a stretch of (40-30) cm
from the work for (35-30) cm and you get the difference.
In other incarnations of this problem, watch out for the
possibility that the "stretch" of the spring is actually traveling
through the natural length, where the spring is
returning energy for a portion of the travel.
Eugene