A wire that is 1.0 mm in diameter and 3.5 m long stretches 3.5 mm when an 8.0-kg tool is hung from it. Given the table below, what material is the wire made from? Young's Modulus (10° N/m²) Material aluminum 70 brass 100 concrete 30 iron 211 nylon 3 rubber band 0.005 steel 200 Concrete Iron Rubber Band Brass O OO O
A wire that is 1.0 mm in diameter and 3.5 m long stretches 3.5 mm when an 8.0-kg tool is hung from it. Given the table below, what material is the wire made from? Young's Modulus (10° N/m²) Material aluminum 70 brass 100 concrete 30 iron 211 nylon 3 rubber band 0.005 steel 200 Concrete Iron Rubber Band Brass O OO O
College Physics
1st Edition
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:Paul Peter Urone, Roger Hinrichs
Chapter5: Further Applications Of Newton's Laws: Friction, Drag, And Elasticity
Section: Chapter Questions
Problem 31PE: (a) The "lead" in pencils is a graphite composition with a Young's modulus of about 1109 N/ m2....
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![**Material Properties and Elongation Calculation**
**Problem Statement:**
A wire that is 1.0 mm in diameter and 3.5 m long stretches 3.5 mm when an 8.0-kg tool is hung from it. Using the table below, determine the material of the wire.
**Table: Young's Modulus for Different Materials**
| Material | Young’s Modulus (10^9 N/m^2) |
|-------------|-------------------------------|
| Aluminum | 70 |
| Brass | 100 |
| Concrete | 30 |
| Iron | 211 |
| Nylon | 3 |
| Rubber Band | 0.005 |
| Steel | 200 |
### Question:
Given the above information, what material is the wire made from?
### Options:
1. Concrete
2. Iron
3. Rubber Band
4. Brass
### Explanation:
To determine the material of the wire, we need to use the given data and the concept of Young's modulus (E), which is a measure of the stiffness of a given material.
**Young's Modulus (E) Calculation:**
\[ E = \frac{{stress}}{{strain}} \]
\[ stress = \frac{Force}{Area} \]
\[ strain = \frac{Extension}{Original Length} \]
\[ Force (F) = mass \times gravity \]
\[ Area (A) = \pi \times (radius)^2 \]
**Given:**
- Diameter (d) = 1.0 mm = 0.001 m
- Radius (r) = d / 2 = 0.0005 m
- Length (L) = 3.5 m
- Extension (ΔL) = 3.5 mm = 0.0035 m
- Mass (m) = 8.0 kg
- Gravity (g) = 9.81 m/s^2 (approx)
**Calculations:**
\[ Force (F) = 8.0 \text{ kg} \times 9.81 \text{ m/s}^2 = 78.48 \text{ N} \]
\[ Area (A) = \pi \times (0.0005 \text{ m})^2 = 7.854 \times 10^{-7} \text{ m}^2 \]
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Transcribed Image Text:**Material Properties and Elongation Calculation**
**Problem Statement:**
A wire that is 1.0 mm in diameter and 3.5 m long stretches 3.5 mm when an 8.0-kg tool is hung from it. Using the table below, determine the material of the wire.
**Table: Young's Modulus for Different Materials**
| Material | Young’s Modulus (10^9 N/m^2) |
|-------------|-------------------------------|
| Aluminum | 70 |
| Brass | 100 |
| Concrete | 30 |
| Iron | 211 |
| Nylon | 3 |
| Rubber Band | 0.005 |
| Steel | 200 |
### Question:
Given the above information, what material is the wire made from?
### Options:
1. Concrete
2. Iron
3. Rubber Band
4. Brass
### Explanation:
To determine the material of the wire, we need to use the given data and the concept of Young's modulus (E), which is a measure of the stiffness of a given material.
**Young's Modulus (E) Calculation:**
\[ E = \frac{{stress}}{{strain}} \]
\[ stress = \frac{Force}{Area} \]
\[ strain = \frac{Extension}{Original Length} \]
\[ Force (F) = mass \times gravity \]
\[ Area (A) = \pi \times (radius)^2 \]
**Given:**
- Diameter (d) = 1.0 mm = 0.001 m
- Radius (r) = d / 2 = 0.0005 m
- Length (L) = 3.5 m
- Extension (ΔL) = 3.5 mm = 0.0035 m
- Mass (m) = 8.0 kg
- Gravity (g) = 9.81 m/s^2 (approx)
**Calculations:**
\[ Force (F) = 8.0 \text{ kg} \times 9.81 \text{ m/s}^2 = 78.48 \text{ N} \]
\[ Area (A) = \pi \times (0.0005 \text{ m})^2 = 7.854 \times 10^{-7} \text{ m}^2 \]
\[
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