A child’s pogo stick stores energy in a spring with spring constant 31200 N/m. At position A (x1 = −0.18 m) the spring compression is a maximum and the child is momentarily at rest. At position B (x = 0 m) the spring is relaxed (no forces acting on it) and the child is moving upward. At position C (x2) the spring is still relaxed and the child is again momentarily at rest at the top of the jump.
A.)Find the total energy of the system if both potential energies are zero at x = 0 (position B). The acceleration due to gravity is 9.8 m/s2 and the combined mass of child and pogo stick is 26 kg. The long dashed line at each position is the relaxed spring equilibrium position. Answer in units of J
B.)Find the maximum height x2 Answer in units of m.
C.)Find the speed of the child at x = 0 Answer in units of m/s
D.) Find the magnitude of x for which the kinetic energy of the system is a maximum. Answer in units of m.
E.) What is the sign of x for which the kinetic energy of the system is a maximum?
1. positive, since x > 0
2. negative, since x < 0
3. neither, since x = 0
F.) Find the child’s maximum upward speed. Answer in units of m/s.