Book edition 2nd Edition

Author(s) Randy Harris

Pages 633 pages

ISBN 9780805303087

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Suppose a force between two particles decreases distance according to $F = k / r^{b}$ . What is the limit on b if the energy required to separate the particles Infinitely far is not to be infinite?

The limit on b is $b > 1$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

A force between two particles decreases with distance, according to $F = k / r^{b}$ .

Step 2: Concept of Potential energy

The force $F_{x}$ is the negative of the derivative of the potential energy U such that,

$F_{x} = - \frac{d U}{d x}$

Therefore, the differential form of the potential energy can be written as,

$d U = - F_{x} d x$

Step 3: Calculation of the potential energy

Integrate the above equation on both sides, andgetthe expression for the total potential energy as:

$U (x) = - \int F_{x} d x$

For force,the formula can be written as:

$F = \frac{k}{r^{b}}$

The energy of this force would be given as,

$U = - \int F d r$

Substitute $F = \frac{k}{r^{b}}$ in the above equation as:

$\begin{array}{rcl} U & = & \int \frac{k}{r^{b}} d r \\ U & = & - \int k r^{- b} d r \\ U & = & - \frac{k r^{- b + 1}}{- b + 1} \end{array}$

When b is not 1 , we need $- b + 1 < 0$ to make sure the energy is not infinite at infinite separation, which is $b > 1$ . Thus, the limit on is $b > 1$

Find Study Materials for

Create Study Materials

Select your language

Modern Physics

Answers without the blur.

Short Answer

Suppose a force between two particles decreases distance according to $F = k / r^{b}$ . What is the limit on b if the energy required to separate the particles Infinitely far is not to be infinite?

Step by Step Solution

Step 1: Given data

Step 2: Concept of Potential energy

Step 3: Calculation of the potential energy

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Modern Physics

Answers without the blur.

Short Answer

Suppose a force between two particles decreases distance according to F=k/rb . What is the limit on b if the energy required to separate the particles Infinitely far is not to be infinite?

Step by Step Solution

Step 1: Given data

Step 2: Concept of Potential energy

Step 3: Calculation of the potential energy

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

Famous Physicists

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

Suppose a force between two particles decreases distance according to $F = k / r^{b}$ . What is the limit on b if the energy required to separate the particles Infinitely far is not to be infinite?