A child\'s pogo stick (figure below) stores energy in a spring (k = 2.6 times 10

Question

A child's pogo stick (figure below) stores energy in a spring (k = 2.6 times 104 N/m). At position (x1 = -0.100 m), the spring compression is a maximum and the child is momentarily at rest. At position (x = 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. Assume that the combined mass of child and pogo stick is 28.0 kg. Calculate the total energy of the system if both potential energies are zero at x = 0. Determine x2. 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. Obtain the child's maximum upward speed.

Explanation / Answer

a)0.5*k*x^2 = 0.5*2.6*10^4*0.1*0.1 = 130J

b)28*9.8*(0.1+x2) = 130

x2 = 130/(28*9.8) - 0.1 = 0.37

c)0.5*28*v^2 + 28*9.8*0.1 = 130

v = sqrt((130-28*9.8*0.1)/14)= 2.7m/s

d) KE is max at x=0.

e)2.7m/s is the maximum upward speed. (when x=0)

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