/*! 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 58 The elastic limit of a piece of ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 58

The elastic limit of a piece of steel wire is \(2.70 \times 10^{9} \mathrm{~Pa}\). What is the maximum speed at which transverse wave pulses can propagate along the wire without exceeding its elastic limit? (The density of steel is \(7.86 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\).)

Short Answer

Expert verified
Maximum transverse wave speed in the steel wire without exceeding the elastic limit is approximately 1862.6 m/s.

Step by step solution

01

Identify given quantities

We are given the elastic limit of steel, \( \sigma = 2.7 \times 10^{9} \, \mathrm{Pa} \), and the density of steel, \( \rho = 7.86 \times 10^{3} \, \mathrm{kg/m^3} \). These values act as stress and density in the wave speed formula.
02

Substitute for \( v \) in wave speed formula

Now, we need to substitute these values into the wave speed formula \( v = \sqrt{\frac{\sigma}{\rho}} \). This gives us \( v = \sqrt{\frac{2.7 \times 10^{9} \, \mathrm{Pa}}{7.86 \times 10^{3} \, \mathrm{kg/m^3}}} \).
03

Calculate the wave speed

By solving this calculation, we obtain the wave speed \( v \). This is the maximum speed at which transverse wave pulses can propagate along the wire without exceeding its elastic limit.

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

An object moves uniformly around a circular path of radius \(20.0 \mathrm{~cm}\), making one complete revolution every \(2.00 \mathrm{~s}\). What are (a) the translational speed of the object, (b) the frequency of motion in hertz, and (c) the angular speed of the object?

A \(50.0-\mathrm{g}\) object is attached to a horizontal spring with a force constant of \(10.0 \mathrm{~N} / \mathrm{m}\) and released from rest with an amplitude of \(25.0 \mathrm{~cm}\). What is the velocity of the object when it is halfway to the equilibrium position if the surface is frictionless?

A spring \(1.50 \mathrm{~m}\) long with force constant \(475 \mathrm{~N} / \mathrm{m}\) is hung from the ceiling of an elevator, and a block of mass \(10.0 \mathrm{~kg}\) is attached to the bottom of the spring. (a) By how much is the spring stretched when the block is slowly lowered to its equilibrium point? (b) If the elevator subsequently accelerates upward at \(2.00 \mathrm{~m} / \mathrm{s}^{2}\), what is the position of the block, taking the equilibrium position found in part (a) as \(y=0\) and upwards as the positive \(y\)-direction. (c) If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion?

The period of motion of an object-spring system is \(T=\) \(0.528 \mathrm{~s}\) when an object of mass \(m=238 \mathrm{~g}\) is attached to the spring. Find (a) the frequency of motion in hertz and (b) the force constant of the spring. (c) If the total energy of the oscillating motion is \(0.234 \mathrm{~J}\), find the amplitude of the oscillations.

A spring in a toy gun has a spring constant of \(9.80 \mathrm{~N} / \mathrm{m}\) and can be compressed \(20.0 \mathrm{~cm}\) beyond the equilibrium position. A \(1.00-\mathrm{g}\) pellet resting against the spring is propelled forward when the spring is released. (a) Find the muzzle speed of the pellet. (b) If the pellet is fired horizontally from a height of \(1.00 \mathrm{~m}\) above the floor, what is its range?
See all solutions

Recommended explanations on Physics Textbooks

Medical Physics

Read Explanation

Mechanics and Materials

Read Explanation

Atoms and Radioactivity

Read Explanation

Electric Charge Field and Potential

Read Explanation

Nuclear Physics

Read Explanation

Physical Quantities And Units

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.