Calculate the work required to stretch the following springs 0.5 m from their equilibrium positions. Assume Hoo is obeyed. a. A spring that required a force of 50 N to be stretched 0.1 m from its equilibrium position. b. A spring that required 40 J of work to be stretched 0.4 m from its equilibrium position.
Calculate the work required to stretch the following springs 0.5 m from their equilibrium positions. Assume Hoo is obeyed. a. A spring that required a force of 50 N to be stretched 0.1 m from its equilibrium position. b. A spring that required 40 J of work to be stretched 0.4 m from its equilibrium position.
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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![**Problem Statement**
Calculate the work required to stretch the following springs 0.5 m from their equilibrium positions. Assume Hooke's law is obeyed.
**a.** A spring that required a force of 50 N to be stretched 0.1 m from its equilibrium position.
**b.** A spring that required 40 J of work to be stretched 0.4 m from its equilibrium position.
---
**Detailed Explanation:**
In these problems, you are asked to calculate the work required to stretch springs, using Hooke's Law, which is defined as:
\[ F = kx \]
where:
- \( F \) is the force applied,
- \( k \) is the spring constant,
- \( x \) is the displacement from the equilibrium position.
The work done on the spring can be calculated using the formula:
\[ W = \frac{1}{2}kx^2 \]
For each of the given scenarios, you'll need to determine the spring constant \( k \), and then use it to calculate the work required for the specified stretch.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8288b48-397c-47a1-92e8-4d9421f21f30%2Fd2f07d75-80c1-4e2b-bbe7-433ce9f4bba3%2Fffdlzit_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
Calculate the work required to stretch the following springs 0.5 m from their equilibrium positions. Assume Hooke's law is obeyed.
**a.** A spring that required a force of 50 N to be stretched 0.1 m from its equilibrium position.
**b.** A spring that required 40 J of work to be stretched 0.4 m from its equilibrium position.
---
**Detailed Explanation:**
In these problems, you are asked to calculate the work required to stretch springs, using Hooke's Law, which is defined as:
\[ F = kx \]
where:
- \( F \) is the force applied,
- \( k \) is the spring constant,
- \( x \) is the displacement from the equilibrium position.
The work done on the spring can be calculated using the formula:
\[ W = \frac{1}{2}kx^2 \]
For each of the given scenarios, you'll need to determine the spring constant \( k \), and then use it to calculate the work required for the specified stretch.
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