61. A child's pogo stick (Fig. P8.61) stores energy in a spring with a force constant of 2.50 X B) 10 N/m. At position (x -0.100 m), the spring com- pression is a maximum and the child is momentarily at rest. At position ® (x = 0), the spring is relaxed and the child is mov- %3D ing upward. At position ©, the child is again momentarily at rest at the top of the jump. The combined mass of child and Figure P8.61 pogo stick is 25.0 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. (a) Calculate the total energy of the child-stick-Earth system, taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine xe. (c) Calculate the speed of the child at x = 0. (d) Determine the value of x for which. the kinetic energy of the system is a maximum. (e) Cal- culate the child's maximum upward speed.

61. A child's pogo stick (Fig. P8.61) stores energy in a spring with a force constant of 2.50 X B) 10 N/m. At position (x -0.100 m), the spring com- pression is a maximum and the child is momentarily at rest. At position ® (x = 0), the spring is relaxed and the child is mov- %3D ing upward. At position ©, the child is again momentarily at rest at the top of the jump. The combined mass of child and Figure P8.61 pogo stick is 25.0 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. (a) Calculate the total energy of the child-stick-Earth system, taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine xe. (c) Calculate the speed of the child at x = 0. (d) Determine the value of x for which. the kinetic energy of the system is a maximum. (e) Cal- culate the child's maximum upward speed.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter7: Conservation Of Energy

Section: Chapter Questions

Problem 69P: A childs pogo stick (Fig. P7.69) stores energy in a spring with a force constant of 2.50 104 N/m....

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A childs pogo stick (Fig. P7.69) stores energy in a spring with a force constant of 2.50 104 N/m. At position (x = 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. The combined mass of child and pogo stick is 25.0 kg. Although the boy must lean forward to remain balanced, the angle is small, so lets assume the pogo stick is vertical. Also assume the boy does not bend his legs during the motion. (a) Calculate the total energy of the childstickEarth system, taking both gravitational and elastic potential energies as zero for x = 0. (b) Determine x. (c) Calculate the speed of the child at x = 0. (d) Determine the value of x for which the kinetic energy of the system is a maximum. (e) Calculate the childs maximum upward speed. Figure P7.69
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