A child\'s pogo stick as shown below stores energy in a spring with a force cons

Question

A child's pogo stick as shown below stores energy in a spring with a force constant of 2.55 Times 10^4 N/m. At position (x_A = -0.120 m), the spring compression is a maximum and the child is momentarily at rest. At position (x_B = 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. The combined mass of the child and the pogo stick is 33.5 kg. Although the boy must lean forward to remain balanced, the angle is small, so let's assume the pogo stick is vertical. Also assume the boy does not bend his legs during the motion. Calculate the total energy of the child-stick-Earth system, taking both gravitational and elastic potential energies as zero for x = 0. Determine x_C Calculate the speed of the child at x = 0. Determine the value of x for which the kinetic energy of the system is a maximum. Calculate the child's maximum upward speed.

Explanation / Answer

a)

x = 0.120 m

k = spring constant = 25500

m = 33.5 kg

Total energy = PE + spring PE = - mg x + (0.5) k x2 = - 33.5 x 9.8 (0.120) + (0.5) (25500) (0.120)2 = 144 J

b)

at C :

using conservation of enery at A and C

Total energy at A = total energy at C

144 = mg xc + (0.5) k xc2

144 = - 33.5 x 9.8 xc + (0.5) (25500) xc2

xc = 0.0942 m

c)

using conservation of enery at A and B

Total energy at A = total energy at B

144 = (0.5) m v2

144 = (0.5) (33.5) v2

V = 2.93 m/s

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