Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 36: Q. 46 (page 1060)

Two events in reference frame S occur 10μs apart at the same point in space. The distance between the two events is 2400min reference frame S'.

a. What is the time interval between the events in reference frame S′?

b. What is the velocity ofS'relative to S?

Short Answer

Expert verified

a. The time interval between the events in the reference frame S'is 12.8μs.

b. The velocity of S' relative to Sis0.480c.

Step by step solution

01

Part (a) Step 1: Given Information

We need to find the time interval between the events in reference frameS'.

02

Part (a) Step 2: Simplify

Consider :

∆x'=2400mt=10×10-6s

We finding time interval between the events in reference frame S':

∆t2=c∆t2-∆x2=c∆t'2-∆x'2c∆t'2=(c×10×10-6)2+24002 c∆t'2=3.02×106+2.42×106c∆t'2=3.02+2.42×106c∆t'2=3.841×103∆t'=3.841×1033×108=12.8μs

03

Part (b) Step 1: Given Information

We need to find the velocity of S'relative toS.

04

Part (b) Step 2: Simplify

The velocity of S'relative to S, as:

t'=γt-νxc2→v=0.480c

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

At what speed, as a fraction of c, would a round-trip astronaut “lose” 125 of the elapsed time shown on her watch?

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′?

The Stanford Linear Accelerator (SLAC) accelerates electrons to v=0.99999997cin a 3.2kmlong tube. If they travel the length of the tube at full speed (they don’t, because they are accelerating), how long is the tube in the electrons’ reference frame?

An astronaut travels to a star system 4.5lyaway at a speed of 0.90c.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?

A ball of mass m traveling at a speed of 0.80c has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass 2m departs the collision with a speed of 0.40c. Let’s do a relativistic collision analysis to determine the mass and speed of the ball after the collision.

a. What is gp, written as a fraction like a/b?

b. What is the initial total momentum? Give your answer as a fraction times mc. c. What is the initial total energy? Give your answer as a fraction times mc2 . Don’t forget that there are two balls.

d. Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is 2m. Instead, let the final state of the system be an unknown mass M traveling at the unknown speed uf. You have two conservation laws. Find M and uf.
See all solutions

Recommended explanations on Physics Textbooks

Wave Optics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Space Physics

Read Explanation

Oscillations

Read Explanation

Linear Momentum

Read Explanation

Kinematics 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