Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A pogo stick has a spring with a force constant of $2.50 \times 10^{4} N / m$ , which can be compressed $12.0 cm$ . To what maximum height can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of $40.0 kg$ ? Explicitly show how you follow the steps in the Problem-Solving Strategies for Energy.

The child can jump up to the maximum height of $0.46 m$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Spring Potential Energy

Spring potential energy: When a spring is stretched or compressed by the application of force, the potential energy stored in the spring is,

${PE}_{s} = \frac{1}{2} k x^{2}$

Here, k is the force constant of the spring $(k = 2.50 \times 10^{4} N / m)$ and x is the compression in the spring 12.0 cm.

Find the maximum height can a child jump

When a child jumps on the spring, the spring potential energy in the spring gets converted into gravitational potential energy and the child attains some height. Mathematically,

${PE}_{s} = {PE}_{g} \frac{1}{2} k x^{2} = m g h$

Here, m is the mass of the child $(m = 40.0 kg)$ , g is the acceleration due to gravity $(g = 9.8 m / s^{2})$ , and h is the maximum height attained by the child.

The expression for the maximum height attained by the child is,

$h = \frac{k x^{2}}{2 m g}$

Putting all known values,

$h = \frac{(2.50 \times 10^{4} N / m) \times {(12.0 cm)}^{2}}{(40.0 kg) \times (9.8 m / s^{2})} = \frac{(2.50 \times 10^{4} N / m) \times {[(12.0 cm) \times (\frac{1 m}{100 cm})]}^{2}}{2 \times (40.0 kg) \times (9.8 m / s^{2})} = 0.46 m$

Therefore, the child can jump up to the maximum height of $0.46 m$ .

Find Study Materials for

Create Study Materials

Select your language

College Physics (Urone)

Answers without the blur.

Short Answer

Step by Step Solution

Spring Potential Energy

Find the maximum height can a child jump

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

College Physics (Urone)

Answers without the blur.

Short Answer

Step by Step Solution

Spring Potential Energy

Find the maximum height can a child jump

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics