College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
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.](https://content.bartleby.com/qna-images/question/da579a50-4d79-460d-b1ac-a80a17754259/dd787388-4527-4678-b71e-0e9e61eaa633/i9u987_processed.png)
Transcribed Image Text:**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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Question 4 of 7 > A particular human hair has a Young's modulus of 3.64 × 10° N/m² and a diameter of 148 μm. If a 217 g object is suspended by the single strand of hair that is originally 15.5 cm long, by how much AL hair will the hair stretch? If the same object were hung from an aluminum wire of the same dimensions as the hair, by how much ALAI would the aluminum stretch? If the strand of hair is modeled as a spring, what is its spring constant khair? AL hair ALAI = Khair = m N/m Question Source: Freedman College Physics 3e | Publisher: Macarrow_forwardIn the figure, a 134 kg uniform log hangs by two steel wires, A and B, both of radius 1.20 mm. Initially, wire A was 2.70 m long and 1.75 mm shorter than wire B: The log is now horizontal. Young's modulus for steel is 2.00 x 1011 N/m² What are the magnitudes of the forces on it from (a) wire A and (b) wire B? (c) What is the ratio da/dg? (a) Number i (b) Number (c) Number Wire A Units Units Units Wire Barrow_forwardMany caterpillars construct cocoons from silk, one of the strongest naturally occurring materials known. Each thread is typically 2.0 µm in diameter, and the silk has a Young's modulus of 4.0 × 10⁹ N/m². Assuming that there is no appreciable space between the parallel strands, how many strands N would be needed to make a rope 8.2 m long that would stretch only 1.02 cm when supporting a pair of 91-kg mountain climbers? N = Again assuming that there is no appreciable space between the parallel strands, what would be the diameter d of the rope? strands d = cmarrow_forward
- A television set rests on four rubber pads, each one having a height of 1.0 cm and a radius of 0.60 cm. If a 200-N horizontal force is applied to the television set, what is the shear stress on each of the pads assuming they do not slide on the floor? O A) 177 N/m2 B) 4.42x105 N/m² O C) 1.77x106 N/m2 D) 44.2 N/m2 acer Pauso Prisc Scrik F12 F11 F10 Home Ins SREATH End UGG Del KEFFECT WAVE# P Enterarrow_forwardAfter a fall, a 74 kg rock climber finds himself dangling from the end of a rope that had been 15 m long and 9.8 mm in diameter but has stretched by 2.4 cm. For the rope, calculate (a) the strain, (b) the stress, and (c) the Young's modulus. (a) Number Units (b) Number i Units (c) Number Unitsarrow_forwardIn the figure, a 110 kg uniform log hangs by two steel wires, A and B, both of radius 1.00 mm. Initially, wire A was 2.50 m long and 1.90 mm shorter than wire B. The log is now horizontal. Young's modulus for steel is 2.00 × 1011 N/m². What are the magnitudes of the forces on it from (a) wire A and (b) wire B? (c) What is the ratio dд/dB? Wire A Wire B comarrow_forward
- A 1.6 x 10-3-kg house spider is hanging vertically by a thread that has a Young's modulus of 4.3 x 109 N/m2 and a radius of 12 x 10-6 m. Suppose that a 96-kg person is hanging vertically on an aluminum (Young's modulus 6.9 x 1010 N/m2) wire. What is the radius of the wire that would exhibit the same strain as the spider's thread, when the thread is stressed by the full weight of the spider?arrow_forwardThe change in dimension of an object under application of external force is strain Is given by the strain ε. Is this statement correct?arrow_forwardRubber has a Young's modiles of 1.5 x 10^8 Pa. If someone were to apply a force of 3 x 10^10 N to the side of a 12 m^3 cube, what would the strain on the cube of rubber bearrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press 
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON