# When a certain spring is stretched, the restoring force satisfies the equation F=-kx+βx^3. If k=10.2N/m and β?

When a certain spring is stretched, the restoring force satisfies the equation F=-kx+βx^3. If k=10.2N/m and β=97N/m^3, calculate the work done by this force when the spring is stretched 0.086m

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- 7 years agoFavorite Answer
F = = -kx+βx^3 , forget about the units for instance.

Work done (W) is:

W = ∫F.dx [From x = 0 to x = 0.086]

W = ∫-kx+βx^3 [From x = 0 to x = 0.086]

W = -k∫x + β∫x^3 [From x = 0 to x = 0.086]

W = -kx^2/2 + βx^4/4 [From x = 0 to x = 0.086]

W = -(10.2)(0.086)^2/2 + (97)(0.086)^4/4

W = -0.0377 + 0.00132

W = -0.03638J

Source(s): It didn't want the work to be negative, that too in conservative forces. Weird...

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