Please solve the question in handwriting step by step
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
Please solve the question in handwriting step by step.
![### Problem Description
4. The position of the automobile jack shown is controlled by a screw ABC that is single-threaded at each end (right-handed thread at A, left-handed thread at C). Each thread has a pitch of 2.5 mm and a mean diameter of 9 mm. If the coefficient of static friction is 0.15, determine the magnitude of the couple \( M \) that must be applied to raise the automobile.
### Diagram Explanation
The diagram shows a mechanical jack system. The system includes:
- A screw ABC controlling the position, with different threads at points A and C.
- A force of 6000 N applied vertically downward at the top of the jack.
- The jack arms form an angle labeled \( 20^\circ \).
- A couple \( M \) is applied at point C to lift the jack.
### Formulas
The following formulas are provided for solving the problem:
\[
\tan \phi = \mu
\]
\[
M = Rr \sin(\phi)
\]
\[
M = rs \cdot r \tan(\phi + \Theta)
\]
\[
\Theta = \tan^{-1} \left(\frac{L}{2\pi}\right) = \tan^{-1} \left(\frac{np}{2\pi}\right)
\]
Where:
- \(\phi\) is the angle of friction.
- \(\mu\) is the coefficient of static friction.
- \(R\) and \(r\) are dimensions related to the screw and thread.
- \(L\) is the lead or advance per rotation.
- \(n\) and \(p\) represent the number of threads and pitch.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e4fcbe0-ed74-4447-b38a-a2af13f9fabc%2F4b5dc987-2c6f-42c8-ab3b-18135a7941fe%2Fsza6gdo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Description
4. The position of the automobile jack shown is controlled by a screw ABC that is single-threaded at each end (right-handed thread at A, left-handed thread at C). Each thread has a pitch of 2.5 mm and a mean diameter of 9 mm. If the coefficient of static friction is 0.15, determine the magnitude of the couple \( M \) that must be applied to raise the automobile.
### Diagram Explanation
The diagram shows a mechanical jack system. The system includes:
- A screw ABC controlling the position, with different threads at points A and C.
- A force of 6000 N applied vertically downward at the top of the jack.
- The jack arms form an angle labeled \( 20^\circ \).
- A couple \( M \) is applied at point C to lift the jack.
### Formulas
The following formulas are provided for solving the problem:
\[
\tan \phi = \mu
\]
\[
M = Rr \sin(\phi)
\]
\[
M = rs \cdot r \tan(\phi + \Theta)
\]
\[
\Theta = \tan^{-1} \left(\frac{L}{2\pi}\right) = \tan^{-1} \left(\frac{np}{2\pi}\right)
\]
Where:
- \(\phi\) is the angle of friction.
- \(\mu\) is the coefficient of static friction.
- \(R\) and \(r\) are dimensions related to the screw and thread.
- \(L\) is the lead or advance per rotation.
- \(n\) and \(p\) represent the number of threads and pitch.
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