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 14: Q. 32 (page 385)

A 70 kg mountain climber dangling in a crevasse stretches a 50-m-long, 1.0-cm-diameter rope by 8.0 cm. What is Young’s modulus for the rope?

Short Answer

Expert verified

Young's modulus of the rope is $5.5 \times 10^{9} N / m^{2}$ .

Step by step solution

01

Given information

The mass of the climber is $m = 70 k g$

$∆ L = 8 c m = 0.08 m$

The length of the rope is $L = 50 m$

The radius of the rope is $r = \frac{1.0 c m}{2} = 0.5 c m = 0.005 m$

02

Tensile stress

The tensile stress is given by $\frac{F}{A}$ .

role="math" localid="1650295387964" $\frac{F}{A} = \frac{m g}{{πr}^{2}} = \frac{70 \times 9.8}{π {(0.005)}^{2}} = 8.73 \times 10^{6} N / m^{2}$

03

Strain

The strain is given by $\frac{∆ L}{L}$ .

$\frac{∆ L}{L} = \frac{0.08}{50} = 0.0016$

04

Young's modulus of the rope

The Young's modulus of the rope is given by $Y = \frac{\frac{F}{A}}{\frac{∆ L}{L}}$ .

Substitute the obtained values

localid="1650296015704" $Y = \frac{8.73 \times 10^{6}}{0.0016} = 5.5 \times 10^{9} N / m^{2}$

Therefore, Young's modulus of the rope is localid="1650296024948" $5.46 \times 10^{9} N / m^{2}$ .

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 $2.0 m L$ syringe has an inner diameter of $6.0 m m$ , a needle inner diameter of 0.25mm, and a plunger pad diameter (where you place your finger) of $1.2 c m$ . A nurse uses the syringe to inject medicine into a patient whose blood pressure is $140 / 100$ .

A. What is the minimum force the nurse needs to apply to the syringe?

B. The nurse empties the syringe in $2.0 s$ . What is the flow speed of the medicine through the needle?

A spring with spring constant 35 N/m is attached to the ceiling, and a 5.0-cm-diameter, 1.0 kg metal cylinder is attached to its lower end. The cylinder is held so that the spring is neither stretched nor compressed, then a tank of water is placed underneath with the surface of the water just touching the bottom of the cylinder. When released, the cylinder will oscillate a few times but, damped by the water, quickly reach an equilibrium position. When in equilibrium, what length of the cylinder is submerged?

It's possible to use the ideal-gas law to show that the density of the earth's atmosphere decreases exponentially with height. That is, $ρ = ρ_{0} \exp (- z / z_{0})$ , where $Z$ is the height above sea level, $ρ_{0}$ is the density at sea level (you can use the Table $14.1$ value), and $z_{0}$ is called the scale height of the atmosphere.

a. Determine the value of $z_{0}$ .

Hint: What is the weight of a column of air?

b. What is the density of the air in Denver, at an elevation of $1600 m$ ? What percent of sea-level density is this?

a. What volume of water has the same mass as 8.0 m³of ethyl alcohol?
b. If this volume of water is in a cubic tank, what is the pressure at the bottom?

A 6.0 m * 12.0 m swimming pool slopes linearly from a 1.0 m depth at one end to a 3.0 m depth at the other. What is the mass of water in the pool?

See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Famous Physicists

Read Explanation

Mechanics and Materials

Read Explanation

Space Physics

Read Explanation

Electric Charge Field and Potential

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