Log out Go to App
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=Υpmc2.

Here, m = mass of particle

c = speed of light

Υp= Lorentz factor

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

E=E0+K

Here, E0=rest mass energy

K = kinetic energy

Substituting both values of total energy in formula :

Υpmc2=E0+K

03

Step 2.

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

Substituting value in formula :

Υpmc2=E0+2E0

We know that E0=mc2

Substituting the value of E0in formula :

Υpmc2=3mc2

Υp=3m

We know that Υp=11-v2c2

Substituting the value of Υpin formula :

11-v2c2=3

1-v2c2=19

v=83c

v=0.943c

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

An electron moving to the right at0.90ccollides with a positron moving to the left at0.90c. The two particles annihilate and produce two gamma-ray photons. What is the wavelength of the photons?

An out-of-control alien spacecraft is diving into a star at a speed of 1.0×108m/s. At what speed, relative to the spacecraft, is the starlight approaching?

One of the important ways in which the Higgs boson was detected at the Large Hadron Collider was by observing a type of decay in which the Higgs—which decays too quickly to be observed directly—is immediately transformed into two photons emitted back to back. Two photons, with momenta 3.31×10-17kgm/s, were detected. What is the mass of the Higgs boson? Give your answer as a multiple of the proton mass.

Derive the Lorentz transformations for tand t'.

Hint: See the comment following Equation 36.22.

Let’s examine whether or not the law of conservation of momentum is true in all reference frames if we use the Newtonian definition of momentum: px=mux. Consider an object A of mass 3m at rest in reference frame S. Object A explodes into two pieces: object B, of mass m, that is shot to the left at a speed of c/2 and object C, of mass 2m, that, to conserve momentum, is shot to the right at a speed of c/4. Suppose this explosion is observed in reference frame S′ that is moving to the right at half the speed of light.

a. Use the Lorentz velocity transformation to find the velocity and the Newtonian momentum of A in S′.

b. Use the Lorentz velocity transformation to find the velocities and the Newtonian momenta of B and C in S′.

c. What is the total final momentum in S′?

d. Newtonian momentum was conserved in frame S. Is it conserved in frame S′?
See all solutions

Recommended explanations on Physics Textbooks

Waves Physics

Read Explanation

Famous Physicists

Read Explanation

Fields in Physics

Read Explanation

Space Physics

Read Explanation

Turning Points in Physics

Read Explanation

Magnetism

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