A 1 Mg container hangs from a 16 mm diameter steel cable. What is the stress in the cable? (Express your answer using four significant figures.) |MPa O =
A 1 Mg container hangs from a 16 mm diameter steel cable. What is the stress in the cable? (Express your answer using four significant figures.) |MPa O =
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
![**Problem Statement:**
A 1 Mg (megagram) container hangs from a 16 mm diameter steel cable. What is the stress in the cable?
(Express your answer using four significant figures.)
\[
\sigma = \underline{\hspace{2cm}} \text{ MPa}
\]
**Explanation:**
- **Given:**
- Mass of the container (\(m\)) = 1 Mg = 1,000 kg
- Diameter of the cable (\(d\)) = 16 mm
- **To Find:** Stress (\(\sigma\)) in the cable, expressed in megapascals (MPa).
- **Formula:**
\[
\sigma = \frac{F}{A}
\]
where:
- \(F\) is the force due to the weight of the container
- \(A\) is the cross-sectional area of the cable
- **Calculation Steps:**
1. Calculate the force (\(F\)) using:
\[
F = m \cdot g
\]
where \(g\) = 9.81 m/s\(^2\) (acceleration due to gravity).
2. Calculate the cross-sectional area (\(A\)) of the cable using:
\[
A = \pi \left(\frac{d}{2}\right)^2
\]
3. Substitute \(F\) and \(A\) into the stress formula to find \(\sigma\).
(Note: Ensure all units are consistent when performing the calculations.)
Please calculate and fill in the stress value in the answer box, expressed in MPa with four significant figures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca543ba1-431b-41e8-8bdd-c0f65bf0b2e6%2Fcde652af-b74d-4290-a262-6c697b28ba55%2Fww7qwq_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A 1 Mg (megagram) container hangs from a 16 mm diameter steel cable. What is the stress in the cable?
(Express your answer using four significant figures.)
\[
\sigma = \underline{\hspace{2cm}} \text{ MPa}
\]
**Explanation:**
- **Given:**
- Mass of the container (\(m\)) = 1 Mg = 1,000 kg
- Diameter of the cable (\(d\)) = 16 mm
- **To Find:** Stress (\(\sigma\)) in the cable, expressed in megapascals (MPa).
- **Formula:**
\[
\sigma = \frac{F}{A}
\]
where:
- \(F\) is the force due to the weight of the container
- \(A\) is the cross-sectional area of the cable
- **Calculation Steps:**
1. Calculate the force (\(F\)) using:
\[
F = m \cdot g
\]
where \(g\) = 9.81 m/s\(^2\) (acceleration due to gravity).
2. Calculate the cross-sectional area (\(A\)) of the cable using:
\[
A = \pi \left(\frac{d}{2}\right)^2
\]
3. Substitute \(F\) and \(A\) into the stress formula to find \(\sigma\).
(Note: Ensure all units are consistent when performing the calculations.)
Please calculate and fill in the stress value in the answer box, expressed in MPa with four significant figures.
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