Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 7

To whom does an object seem greater in length, an observer moving with the object or an observer moving relative to the object? Which observer measures the object's proper length?

Short Answer

Expert verified
The object seems greater in length to Observer A, who is moving with the object, since this observer is at rest relative to the object and does not experience time dilation or length contraction. Observer A also measures the object's proper length. On the other hand, Observer B, who is moving relative to the object, perceives a shorter length due to time dilation and length contraction.

Step by step solution

01

Understand the concept of length contraction

Length contraction is a phenomenon in special relativity where the length of an object appears to be shorter when it is measured by an observer who is in relative motion with respect to the object. This phenomenon occurs because the observer moving relative to the object experiences time dilation, which causes the object to appear contracted in the direction of motion.
02

Determine the observers and their respective perceptions of length

We have two observers in this scenario: 1. Observer A: moving with the object 2. Observer B: moving relative to the object Now we need to determine which observer perceives a greater length for the object.
03

Identify the observer who perceives a greater length for the object

Observer A, who is moving with the object, is at rest relative to the object, and thus does not experience time dilation or length contraction. Therefore, the object seems to be in its actual (proper) length to Observer A. Observer B, on the other hand, is in relative motion with respect to the object. Due to time dilation and length contraction, Observer B perceives a shorter length for the object than its proper length. Based on this information, we can conclude that the object seems greater in length to Observer A (moving with the object) than to Observer B (moving relative to the object).
04

Identify which observer measures the object's proper length

As mentioned in Step 3, Observer A, who is moving with the object, perceives the object in its actual (proper) length. Therefore, Observer A measures the object's proper length. In conclusion, the object seems greater in length to the observer moving with the object (Observer A) and Observer A also measures the object's proper length.

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 supemova explosion of a \(2.00 \times 10^{31} \mathrm{kg}\) star produces \(1.00 \times 10^{44} \mathrm{J} \quad\) of energy. (a) How many kilograms of mass are converted to energy in the explosion? (b) What is the ratio \(\Delta m / m\) of mass destroyed to the original mass of the star?

(a) Calculate the energy released by the destruction of \(1.00 \mathrm{kg}\) of mass. (b) How many kilograms could be lifted to a \(10.0 \mathrm{km}\) height by this amount of energy?

A spacecraft starts from being at rest at the origin and accelerates at a constant rate \(g\), as seen from Earth, taken to be an inertial frame, until it reaches a speed of \(c / 2\). (a) Show that the increment of proper time is related to the elapsed time in Earth's frame by: \(d \tau=\sqrt{1-v^{2} / c^{2}} d t\) (b) Find an expression for the elapsed time to reach speed C/2 as seen in Earth's frame. (c) Use the relationship in (a) to obtain a similar expression for the elapsed proper time to reach \(c / 2\) as seen in the spacecraft, and determine the ratio of the time seen from Earth with that on the spacecraft to reach the final speed.

(a) What is the momentum of a 2000-kg satellite orbiting at \(4.00 \mathrm{km} / \mathrm{s}\) ? (b) Find the ratio of this momentum to the classical momentum. (Hint: Use the approximation that \(\gamma=1+(1 / 2) v^{2} / c^{2}\) at low velocities.)

(a) Calculate the speed of a 1.00 - \(\mu\) g particle of dust that has the same momentum as a proton moving at \(0.999 c\) (b) What does the small speed tell us about the mass of a proton compared to even a tiny amount of macroscopic matter?
See all solutions

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Read Explanation

Particle Model of Matter

Read Explanation

Modern Physics

Read Explanation

Work Energy and Power

Read Explanation

Circular Motion and Gravitation

Read Explanation

Linear Momentum

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