Solved: A childs pogo stick (Fig. P5.81) stores energy in

Chapter 5, Problem 5.3.81

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A childs pogo stick (Fig. P5.81) stores energy in a spring (k 5 2.50 3 104 N/m). At position _ (x1 5 20.100 m), the spring compression is a maximum and the child is momentarily at rest. At position _ (x 5 0), the spring is relaxed and the child is moving upward. At position _, the child is again momentarily at rest at the top of the jump. Assuming that the combined mass of child and pogo stick is 25.0 kg, (a) calculate the total energy of the system if both potential energies are zero at x 5 0, (b) determine x2, (c) calculate the speed of the child at x 5 0, (d) determine the value of x for which the kinetic energy of the system is a maximum, and (e) obtain the childs maximum upward speed.