**Problem Statement:**A piece of mohair taken from an Angora goat has a radius of \(3 \times 10^{-5}\) m. What is the least number of identical pieces of mohair needed to suspend a 79-kg person, so the strain experienced by each piece is less than 0.010? Assume that the tension is the same in all the pieces.**Solution Approach:**1. **Calculate the stress (σ)** on a single mohair fiber: \[ \sigma = \frac{F}{A} \] where \( F \) is the force exerted by the person's weight (mass \(\times\) gravity), and \( A \) is the cross-sectional area of the mohair fiber ( \( \pi r^2 \) ).2. **Determine the number of pieces (n) needed** such that the strain (ɛ) experienced by each is less than 0.010: \[ \epsilon = \frac{\sigma}{E} \] where \( E \) is Young's modulus of mohair.3. Reorganize the equation and solve for \( n \).**Key Assumptions:**- The tension is equally distributed among all pieces.- Young's modulus of mohair is provided or known from material properties.**Graph and Diagram Description:**- No graphs or diagrams present in this problem statement. This problem involves concepts of material science and strength of materials, particularly understanding mechanical stress, strain, and elasticity.

Strain experienced by each piece is , Mass of the person, Radius, Y= Youngs Modulus = 2.9*10^9Number…

A piece of mohair taken from an Angora goat has a radius of 31x10°° m. What is the least number of identical pieces of mohair needed to suspend a 79-kg person, so the strain experienced by each piece is less than 0.010? Assume that the tension is the same in all the pieces.

A piece of mohair taken from an Angora goat has a radius of 31x10°° m. What is the least number of identical pieces of mohair needed to suspend a 79-kg person, so the strain experienced by each piece is less than 0.010? Assume that the tension is the same in all the pieces.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Mechanical Properties of Solids

There are three types of matter- solid, liquid and gas. Out of them, solids have a rigid shaped and size. The intermolecular forces of attractions in solids are greatest. Mechanical properties are the physical properties of a material which it shows, when it is provided with certain amount of force or load. These properties are to be kept in mind for various purposes. When a force is applied to an object, the object may or may not get deformed depending upon its elastic property. But every time the object develops a restoring force against the force applied. This is commonly known as stress. If the object changes its dimensions due to the force applied it develops strain ( which is the ratio of change in dimension to the original dimension).

Question

**Problem Statement:**

A piece of mohair taken from an Angora goat has a radius of \(3 \times 10^{-5}\) m. What is the least number of identical pieces of mohair needed to suspend a 79-kg person, so the strain experienced by each piece is less than 0.010? Assume that the tension is the same in all the pieces.

**Solution Approach:**

1. **Calculate the stress (σ)** on a single mohair fiber:
\[
\sigma = \frac{F}{A}
\]
where \( F \) is the force exerted by the person's weight (mass \(\times\) gravity),
and \( A \) is the cross-sectional area of the mohair fiber ( \( \pi r^2 \) ).

2. **Determine the number of pieces (n) needed** such that the strain (ɛ) experienced by each is less than 0.010:
\[
\epsilon = \frac{\sigma}{E}
\]
where \( E \) is Young's modulus of mohair.

3. Reorganize the equation and solve for \( n \).

**Key Assumptions:**
- The tension is equally distributed among all pieces.
- Young's modulus of mohair is provided or known from material properties.

**Graph and Diagram Description:**
- No graphs or diagrams present in this problem statement.

This problem involves concepts of material science and strength of materials, particularly understanding mechanical stress, strain, and elasticity.

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