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Homework Statement
If it requires 5.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additioanl 4.0 cm?
Homework Equations
Force done on spring: ##F_P = kx ##
Work: ##\frac {1}{2}kx^2 ##
The Attempt at a Solution
I solved for K and got 25000.
Plugging it into the equation for the work on a spring, I get ##\frac {1}{2}(25000)(0.06)^2 ## where 0.06 is the total length stretched. Doing it that way, I get the right answer.
However, why can't I use the original information (5 J) and simply add it to the remaining 4 cm? ##5 + \frac {1}{2}(25000)(0.04)^2 ## Work is area under the force/displacement graph. Therefore, both ways should work, but that's the case.