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 2.40 104 N/m. At position A (xA = -0.140 m), the spring compression is a maximum and the child is momentarily at rest. At position B (xB = 0), the spring is relaxed and the child is moving upward. At position C, the child is again momentarily at rest at the top of the jump. The combined mass of the child and the pogo stick is 26.0 kg.

(d) Determine the value of x for which the kinetic energy of the system is a maximum.
answer in mm
(e) Calculate the child's maximum upward speed.
answer in m/s

Explanation / Answer

At position A: PE = -mg*(0.14) EE = 1/2 k * (0.14)^2 KE = 0 Total energy, TE = sum of above xC is when KE and EE = 0 ie PE = mgxC = TE solve for xC. When x = 0, EE = 0, and PE = 0 KE = TE = 1/2 mv^2 solve for v To find maximum upward speed, we need to find maximum KE OR minimum PE+EE. PE + EE = -mgx + 1/2 k * x^2 Find x which minimizes this expression. Alternatively, KE + PE + EE = constant 1/2 mv^2 + mgx + kx^2 /2 = constant differentiate wrt time mv * dv/dt - mg*v - kx*v = 0 When v is max, dv/dt = 0 solve for x then find v

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