A certain spring is found not to obey Hookes law; it
Chapter 7, Problem 7.67(choose chapter or problem)
A certain spring is found not to obey Hooke’s law; it exerts a restoring force \(F_{x}(x)=-\alpha x-\beta x^{2}\) if it is stretched or compressed, where \(\alpha=60.0 \mathrm{~N} / \mathrm{m} \text { and } \beta=18.0 \mathrm{~N} / \mathrm{m}^{2}\). The mass of the spring is negligible.
(a) Calculate the potential-energy funcion 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 equilibrium position?
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