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Chapter 10: Problem 16

The maximum strain of a steel wire with Young's modulus $2.0 \times 10^{11} \mathrm{N} / \mathrm{m}^{2},\( just before breaking, is \)0.20 \%$ What is the stress at its breaking point, assuming that strain is proportional to stress up to the breaking point?

Short Answer

Expert verified
Answer: The stress at the breaking point of the steel wire is \(4.0 \times 10^8 \mathrm{N/m^2}\).

Step by step solution

01

Convert strain to decimal form

To find the stress, the first step is to convert the given strain percentage value to decimal form. To do this, simply divide the given percentage value by 100. The strain in decimal form is: $$ \text{strain in decimal} = \frac{0.20\%}{100} = 2.0 \times 10^{-3} $$
02

Calculate stress using Young's modulus and strain

Now that we have the strain value in decimal form, we can use the relationship between stress, Young's modulus, and strain to find the stress at the breaking point. The equation that connects stress, strain, and Young's modulus is: $$ \text{stress} = \text{Young's modulus} \times \text{strain} $$ Substituting the given values, we get: $$ \text{stress} = (2.0 \times 10^{11} \mathrm{N/m^2}) \times (2.0 \times 10^{-3}) $$
03

Calculate the stress at the breaking point

Using the equation from Step 2, we will multiply the Young's modulus and the strain in decimal form to find the stress at the breaking point: $$ \text{stress} = (2.0 \times 10^{11} \mathrm{N/m^2}) \times (2.0 \times 10^{-3}) = 4.0 \times 10^8 \mathrm{N/m^2} $$ So, the stress at the breaking point of the steel wire is \(4.0 \times 10^8 \mathrm{N/m^2}\).

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Most popular questions from this chapter

An object of mass \(306 \mathrm{g}\) is attached to the base of a spring, with spring constant \(25 \mathrm{N} / \mathrm{m},\) that is hanging from the ceiling. A pen is attached to the back of the object, so that it can write on a paper placed behind the mass-spring system. Ignore friction. (a) Describe the pattern traced on the paper if the object is held at the point where the spring is relaxed and then released at \(t=0 .\) (b) The experiment is repeated, but now the paper moves to the left at constant speed as the pen writes on it. Sketch the pattern traced on the paper. Imagine that the paper is long enough that it doesn't run out for several oscillations.
Spider silk has a Young's modulus of $4.0 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}\( and can withstand stresses up to \)1.4 \times 10^{9} \mathrm{N} / \mathrm{m}^{2} . \mathrm{A}$ single webstrand has across-sectional area of \(1.0 \times 10^{-11} \mathrm{m}^{2}\) and a web is made up of 50 radial strands. A bug lands in the center of a horizontal web so that the web stretches downward. (a) If the maximum stress is exerted on each strand, what angle \(\theta\) does the web make with the horizontal? (b) What does the mass of a bug have to be in order to exert this maximum stress on the web? (c) If the web is \(0.10 \mathrm{m}\) in radius, how far down does the web extend? (IMAGE NOT COPY)
The amplitude of oscillation of a pendulum decreases by a factor of 20.0 in \(120 \mathrm{s}\). By what factor has its energy decreased in that time?
A baby jumper consists of a cloth seat suspended by an elastic cord from the lintel of an open doorway. The unstretched length of the cord is $1.2 \mathrm{m}\( and the cord stretches by \)0.20 \mathrm{m}$ when a baby of mass \(6.8 \mathrm{kg}\) is placed into the seat. The mother then pulls the seat down by \(8.0 \mathrm{cm}\) and releases it. (a) What is the period of the motion? (b) What is the maximum speed of the baby?

An acrobat of mass \(55 \mathrm{kg}\) is going to hang by her teeth from a steel wire and she does not want the wire to stretch beyond its elastic limit. The elastic limit for the wire is \(2.5 \times 10^{8} \mathrm{Pa} .\) What is the minimum diameter the wire should have to support her?
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