The combined mass of the child and the pogo stick is 43.8 kg. Although the child...

 

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The combined mass of the child and the pogo stick is 43.8 kg. Although the child must lean forward to remain balanced, the angle is small, so let's assume the pogo stick is vertical. Also assume he does not bend his legs during the motion. (a) Calculate the total mechanical energy of the preteen-stick-Earth system (in J), taking both gravitational and elastic potential energies as zero for x = 0. 222.4 (b) Determine xc (in m). 0.52 m (c) Calculate the speed of the child (in m/s) at x = 0. 3.19 m/s (d) Determine the value of x (in mm) for which the kinetic energy of the system is a maximum. Enter a number. self that the maximum kinetic energy will occur when the spring is compressed and then write an expression for the total mechanical energy when the spring is compressed. Solve this expression for the kinetic energy as a function of the position. Differentiate the kinetic energy with respect to the position and set this equal to zero to determine the position for maximum kinetic energy. mm (e) Calculate the child's maximum upward speed (in m/s). m/s As shown in the figure below, a preteen is playing with a pogo stick that has a spring with a force constant of 2.55 x 104 N/m. At position A (x = -0.150 m), the spring compression is a maximum and the child is momentarily at rest. At position B (x = 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. B A The combined mass of the child and the pogo stick is 43.8 kg. Although the child must lean forward to remain balanced, the angle is small, so let's assume the pogo stick is vertical. Also assume he does not bend his legs during the motion. (a) Calculate the total mechanical energy of the preteen-stick-Earth system (in J), taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine xc (in m). m The combined mass of the child and the pogo stick is 43.8 kg. Although the child must lean forward to remain balanced, the angle is small, so let's assume the pogo stick is vertical. Also assume he does not bend his legs during the motion. (a) Calculate the total mechanical energy of the preteen-stick-Earth system (in J), taking both gravitational and elastic potential energies as zero for x = 0. 222.4 (b) Determine xc (in m). 0.52 m (c) Calculate the speed of the child (in m/s) at x = 0. 3.19 m/s (d) Determine the value of x (in mm) for which the kinetic energy of the system is a maximum. Enter a number. self that the maximum kinetic energy will occur when the spring is compressed and then write an expression for the total mechanical energy when the spring is compressed. Solve this expression for the kinetic energy as a function of the position. Differentiate the kinetic energy with respect to the position and set this equal to zero to determine the position for maximum kinetic energy. mm (e) Calculate the child's maximum upward speed (in m/s). m/s As shown in the figure below, a preteen is playing with a pogo stick that has a spring with a force constant of 2.55 x 104 N/m. At position A (x = -0.150 m), the spring compression is a maximum and the child is momentarily at rest. At position B (x = 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. B A The combined mass of the child and the pogo stick is 43.8 kg. Although the child must lean forward to remain balanced, the angle is small, so let's assume the pogo stick is vertical. Also assume he does not bend his legs during the motion. (a) Calculate the total mechanical energy of the preteen-stick-Earth system (in J), taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine xc (in m). m