Question

05.3 Consider a spring that does not obey Hooke's law very faithfully. One end of the...

05.3 Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with xcomponent Fx =kx – bx2 + cx3 must be applied to the free end, where k = 130 N/m, b = 660 N/m2 , and c = 16000 N/m3 . Note that x > 0 when the spring is stretched and x < 0 when it is compressed. (Many real springs behave in a similar fashion.)

(a) How much work must be done to stretch this spring by 0.050 m from its unstretched length?

(b) How much work must be done to compress this spring by 0.050 m from its unstretched length?

(c) How much work must be done to move the spring from being compressed by 0.070 m to being stretched by 0.030 m, assuming the end moves with constant speed during the motion?

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