CALC A certain spring found not to obey Hooke’s law exerts a restoring force Fx(x) = -?x - ?x2 if it is stretched or compressed, where ? = 60.0 N/m and ? = 18.0 Nm2. The mass of the spring is negligible. (a) Calculate the potential-energy function U(x) for this spring. Let U = 0 when x = 0. (b) An object with mass 0.900 kg on a frictionless, horizontal surface is attached to this spring, pulled a distance 1.00 m to the right (the +x-direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the x = 0 equilibrium position?

Solution 67P Problem (a) Step 1: Fx(x) = -x - x -----(1) = 60.0N/m = 18.0N/m 2 The spring does not obey Hooke’s Law Mass of string is negligible