Physics Elastic Energy?
The force exerted by an unusual spring when it is compressed a distance x from equilibrium is given by F = -kx - cx3, where k = 200 N/m and c = 3.6 kN/m3. Find the energy stored in the spring when it has been compressed 13 cm.
Update:Equation should read:
F = -kx - cx^3, where k = 200 N/m and c = 3.6 kN/m^3
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You must integrate the force:
Energy(X) =
integral of work =
integral of -F(x)dx =
integral [from x=0 to x=X] of (kx + cx³)dx
Integration of function (kx + cx³) is very simple task, please, do it yourself.
You are explicitly given everything that you need to know in order to solve this problem. The only thing that you need to watch out for is that the units match (N vs. kN and cm vs. m). Just convert all your values into the same units and then plug them into the given equation. Simple!