/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 60 Octavio, traveling at a speed of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 60

Octavio, traveling at a speed of \(0.60 c,\) passes Tracy and her barn. Tracy, who is at rest with respect to her barn, says that the barn is 16 m long in the direction in which Octavio is traveling, \(4.5 \mathrm{m}\) high, and $12 \mathrm{m}$ deep. (a) What does Tracy say is the volume of her barn? (b) What volume does Octavio measure?

Short Answer

Expert verified
Answer: The volume of the barn measured by Tracy is 864 m鲁, while Octavio measures the volume as 691.2 m鲁.

Step by step solution

01

Calculate the volume of the barn according to Tracy

Since Tracy is at rest relative to the barn, we can use the given dimensions to calculate the barn's volume: Volume = Length 脳 Width 脳 Height Tracy's measured volume = \(16\text{m} \times 4.5\text{m} \times 12\text{m}\)
02

Calculate Tracy's measured volume

Plugging the values into the equation, we get the volume as measured by Tracy: Tracy's measured volume = \(16\text{m} \times 4.5\text{m} \times 12\text{m} = 864\text{m}^3\)
03

Apply length contraction to the barn's length

To find the length of the barn as measured by Octavio, we need to use the length contraction equation: Contracted length = Length / \(\gamma\) Here, \(\gamma = \frac{1}{\sqrt{1 - (v/c)^2}}\), and Octavio's velocity (v) is given as \(0.6c\).
04

Calculate the gamma factor

We can calculate \(\gamma\) using the given velocity: \(\gamma = \frac{1}{\sqrt{1 - (0.6c/c)^2}} = \frac{1}{\sqrt{1 - 0.36}}\)
05

Compute the gamma factor

Solve the expression for the gamma factor: \(\gamma = \frac{1}{\sqrt{0.64}} = \frac{1}{0.8} = 1.25\)
06

Calculate the contracted length

Now, we can find the contracted length using the length contraction equation: Contracted length = \(\frac{16\text{m}}{1.25} = 12.8\text{m}\)
07

Calculate the volume of the barn according to Octavio

Lastly, we can calculate the volume of the barn as measured by Octavio by multiplying the contracted length with the unchanged height and depth: Octavio's measured volume = \(12.8\text{m} \times 4.5\text{m} \times 12\text{m}\)
08

Find Octavio's measured volume

Solve for the volume as measured by Octavio: Octavio's measured volume = \(12.8\text{m} \times 4.5\text{m} \times 12\text{m} = 691.2\text{m}^3\) To summarize the results: (a) Tracy says the volume of her barn is \(864\text{m}^3\) (b) Octavio measures the volume of the barn as \(691.2\text{m}^3\)

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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 spaceship travels at constant velocity from Earth to a point 710 ly away as measured in Earth's rest frame. The ship's speed relative to Earth is $0.9999 c .$ A passenger is 20 yr old when departing from Earth. (a) How old is the passenger when the ship reaches its destination, as measured by the ship's clock? (b) If the spaceship sends a radio signal back to Earth as soon as it reaches its destination, in what year, by Earth's calendar, does the signal reach Earth? The spaceship left Earth in the year 2000.
A cosmic ray particle travels directly over a football field, from one goal line to the other, at a speed of \(0.50 c .\) (a) If the length of the field between goal lines in the Earth frame is \(91.5 \mathrm{m}(100 \mathrm{yd}),\) what length is measured in the rest frame of the particle? (b) How long does it take the particle to go from one goal line to the other according to Earth observers? (c) How long does it take in the rest frame of the particle?
An engineer in a train moving toward the station with a velocity \(v=0.60 c\) lights a signal flare as he reaches a marker \(1.0 \mathrm{km}\) from the station (according to a scale laid out on the ground). By how much time, on the stationmaster's clock, does the arrival of the optical signal precede the arrival of the train?
The rest energy of an electron is \(0.511 \mathrm{MeV} .\) What momentum (in MeV/c) must an electron have in order that its total energy be 3.00 times its rest energy?
A muon with rest energy 106 MeV is created at an altitude of \(4500 \mathrm{m}\) and travels downward toward Earth's surface. An observer on Earth measures its speed as \(0.980 c .\) (a) What is the muon's total energy in the Earth observer's frame of reference? (b) What is the muon's total energy in the muon's frame of reference?
See all solutions

Recommended explanations on Physics Textbooks

Solid State Physics

Read Explanation

Quantum Physics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Modern Physics

Read Explanation

Rotational Dynamics

Read Explanation

Mechanics and Materials

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.