**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. Concrete2. Iron3. Rubber Band4. 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:**\[ Force (F) = 8.0 \text{ kg} \times 9.81 \text{ m/s}^2 = 78.48 \text{ N} \]\[ Area (A) = \pi \times (0.0005 \text{ m})^2 = 7.854 \times 10^{-7} \text{ m}^2 \]\[

Given data diameter of wire d = 1.0 mm Radius of wire r = 0.5 mm = 0.5 x 10-3 m Cross section area…

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

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

**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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