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. 40 (page 1060)

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

Short Answer

Expert verified

The speed of particle is 0.866c.

Step by step solution

01

Given information

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

02

Step 1.

We know that the formula of total energy is :

$E = Υ_{p} m c^{2}$

Here, m = mass of particle

v = velocity of particle

$Υ_{p}$ = Lorentz factor

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

$E = 2 E_{0}$

Here $E$ = total energy

$E_{0}$ = rest mass energy

03

Step 2.

Substituting $E = 2 E_{0}$ in the formula of total energy :

$2 m c^{2} = Υ_{p} m c^{2}$

$Υ_{p} = 2$

We know that $Υ_{p} = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$ , substituting this value of $Υ_{p}$ :

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

$\frac{v^{2}}{c^{2}} = \frac{3}{4}$

$v = 0.866 c$

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

Bjorn is standing at $x = 600 m$ . Firecracker $1$ explodes at the origin and firecracker $2$ explodes at $x = 900 m$ . The flashes from both explosions reach Bjorn’s eye at $t = 3.0 μ s$ . At what time did each firecracker explode?

Firecracker A is $300 m$ from you. Firecracker B is $600 m$ from you in the same direction. You see both explode at the same time. Define event 1 to be “firecracker A explodes” and event 2 to be “firecracker B explodes.” Does event 1 occur before, after, or at the same time as event 2? Explain.

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

A modest supernova (the explosion of a massive star at the end of its life cycle) releases 1.5 * 1044 J of energy in a few seconds. This is enough to outshine the entire galaxy in which it occurs. Suppose a star with the mass of our sun collides with an antimatter star of equal mass, causing complete annihilation. What is the ratio of the energy released in this star-antistar collision to the energy released in the supernova?

The star Alpha goes supernova. Ten years later and $100 l y$ away, as measured by astronomers in the galaxy, star Beta explodes.

a. Is it possible that the explosion of Alpha is in any way responsible for the explosion of Beta? Explain.

b. An alien spacecraft passing through the galaxy finds that the distance between the two explosions is $120 l y$ . According to the aliens, what is the time between the explosions?

See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Radiation

Read Explanation

Engineering Physics

Read Explanation

Medical Physics

Read Explanation

Magnetism

Read Explanation

Energy Physics

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