Calculate the child\'s maximum upward speed. m/s?? A child\'s pogo stick as show
ID: 1970565 • Letter: C
Question
Calculate the child's maximum upward speed. m/s??
A child's pogo stick as shown below stores energy in a spring with a force constant of 2.55 104 N/m. At position a (xA = -0.110 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. 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 child's maximum upward speed. m/s??Explanation / Answer
The total energy stored in the spring (U) = 1/2 * k * x^2 All of this energy will be converted into kinetic energy U = (1/2) * 25,500 N/m * (0.110 m)^2 = 154.275 Joules So all of that energy will be converted into kinetic energy because the total energy in the system will remain constant (in an idealized scenario) KE = 1/2 * m * v^2 = (1/2) * 26 kg * v^2 = 154.275 Joules v = 3.445 m/s ------ If the above answer is wrong, then you may also need to take into account the change in potential energy ---- PE changes by mass * gravity * height = 26 kg * 9.8 m/s/s * .110 m = 28.028 Joules so 1/2 * 26 * v^2 = 154.275-28.028 v = 3.116 m/s I'm curious to see which of the 2 is correct.
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