Chapter 6, Problem 6.70P

CALC 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 x-component F_x = kx − bx² + cx³ must be applied to the free end. Here k = 100 N/m, b = 700 N/m², and c = 12,000 N/m³. Note that x > 0 when the spring is stretched and x < 0 when it is compressed. How much work must be done (a) to stretch this spring by 0.050 m from its unstretched length? (b) To compress this spring by 0.050 m from its unstretched length? (c) Is it easier to stretch or compress this spring? Explain why in terms of the dependence of F_x on x. (Many real springs behave qualitatively in the same way.)