Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks

Exams
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology

EXAM TYPES

GCSE

IGCSE

AS

A Level

International A Level

University Admissions Tests

GCSE SUBJECTS

GCSE 1

GCSE 2

GCSE 3

GCSE 4

GCSE 5

SOME-TEXT

IGCSE SUBJECTS

IGCSE 1

AS SUBJECTS

AS 1

A Level SUBJECTS

A Level 1

International A Level SUBJECTS

International A Level 1

University Admissions Tests SUBJECTS

University Admissions Tests 1
Features
Features

Discover all of these amazing features with a free account.

Flashcards

Vaia AI

Notes

Study Plans

Study Sets
What’s new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
Resources
Discover

All the hacks around your studies and career - in one place.

Find a job

Find a degree

Student Deals

Magazine

Mobile App
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

Job Board
The largest student job board with the most exciting opportunities.

Vaia Deals
Verified student deals from top brands.

Our App
Discover our mobile app to take your studies anywhere.

Go to App

Learning Materials

Features

Discover

Chapter 36: Q. 39 (page 1060)

At what speed, as a fraction of c, is a particle’s kinetic energy twice its rest energy?

Short Answer

Expert verified

The speed of particle is 0.943c.

Step by step solution

01

Given information

We have given that particle’s kinetic energy twice its rest energy.

02

Step 1.

The formula of total energy is $E = Υ_{p} m c^{2}$ .

Here, m = mass of particle

c = speed of light

$Υ_{p}$ = Lorentz factor

We know that total energy is the sum of rest mass energy and kinetic energy.

$E = E_{0} + K$

Here, $E_{0}$ =rest mass energy

K = kinetic energy

Substituting both values of total energy in formula :

$Υ_{p} m c^{2} = E_{0} + K$

03

Step 2.

We have given that kinetic energy is twice of rest mass energy.

Substituting value in formula :

$Υ_{p} m c^{2} = E_{0} + 2 E_{0}$

We know that $E_{0} = m c^{2}$

Substituting the value of $E_{0}$ in formula :

$Υ_{p} m c^{2} = 3 m c^{2}$

$Υ_{p} = 3 m$

We know that $Υ_{p} = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

Substituting the value of $Υ_{p}$ in formula :

$\frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = 3$

$1 - \frac{v^{2}}{c^{2}} = \frac{1}{9}$

$v = \frac{\sqrt{8}}{3} c$

$v = 0.943 c$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A typical nuclear power plant generates electricity at the rate of $1000 MW$ . The efficiency of transforming thermal energy into electrical energy is $\frac{1}{3}$ and the plant runs at full capacity for $80 %$ of the year. (Nuclear power plants are down about $20 %$ of the time for maintenance and refueling.)

a. How much thermal energy does the plant generate in one year?

b. What mass of uranium is transformed into energy in one year?

Two rockets, $A$ and , approach the earth from opposite directions at speed of $0.80 c$ . The length of each rocket measured in its rest frame is $100 m$ . What is the length of rocket $A$ as measured by the crew of rocket $B$ ?

The quantity dE/dv, the rate of increase of energy with speed, is the amount of additional energy a moving object needs per $1 m / s$ increase in speed.

a. $A 25, 000 k g$ kg truck is traveling at $30 m / s$ . How much additional energy is needed to increase its speed by $1 m / s$ ?

b. $A 25, 000 k g$ rocket is traveling atrole="math" localid="1649677033976" $0.90 c$ . How much additional energy is needed to increase its speed by $1 m / s$ ?

At what speed, as a fraction of c, is a particle’s total energy twice its rest energy?

An astronaut travels to a star system $4.5 l y$ away at a speed of $0.90 c .$ Assume that the time needed to accelerate and decelerate is negligible.

a. How long does the journey take according to Mission Control on earth?

b. How long does the journey take according to the astronaut?

c. How much time elapses between the launch and the arrival of the first radio message from the astronaut saying that she has arrived?

See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Radiation

Read Explanation

Quantum Physics

Read Explanation

Measurements

Read Explanation

Famous Physicists

Read Explanation

Physical Quantities And Units

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free