Chapter 8, Problem 84P

A certain spring is found not to conform to Hooke’s law. The force (in newtons) it exerts when stretched a distance x (in meters) is found to have magnitude 52.8x + 38.4x² in the direction opposing the stretch. (a) Compute the work required to stretch the spring from x = 0.500 m to x = 1.00 m. (b) With one end of the spring fixed, a particle of mass 2.17 kg is attached to the other end of the spring when it is stretched by an amount x = 1.00 m. If the particle is then released from rest, what is its speed at the instant the stretch in the spring is x = 0.500 m? (c) Is the force exerted by the spring conservative or nonconservative? Explain.