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? = kxx? 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. (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) Is it easier to stretch or compress this spring? Explain why in terms of the dependence of F? on x. (Many real springs behave qualitatively in x? the same way.)

Solution 74P Introduction The force as a function of stretch is given, we have to calculate the work done to stretch the spring. Step 1 The work done is given by Now the force is given by Step 2 During stretching we have x = 0 and x = 0.050 m. 1 2 Hence the work done during stretching can be written as Now putting the values of a, b, c we have So, 0.126 J of work must be done to stretch the spring by 0.050 m.