A child's pogo stick (figure below) stores energy in a spring (k = 2.30 x 104 N/m). At position (x₁ = -0.100 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 Ⓒ, 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.

A child's pogo stick (figure below) stores energy in a spring (k = 2.30 x 104 N/m). At position (x₁ = -0.100 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 Ⓒ, 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.

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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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

(x₁ = -0.100 m), the spring compression
A child's pogo stick (figure below) stores energy in a spring (k = 2.30 x 104 N/m). At position
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
Ⓒ, 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.
L="
(b) Determine X₂.
m
amm
(a) Calculate the total energy of the system if both potential energies are zero at x = 0.
]]
(c) Calculate the speed of the child at x = 0.
m/s
(d) Determine the value of x for which the kinetic energy of the system is a maximum.
mm
(e) Obtain the child's maximum upward speed.
m/s

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