The wedge in (Figure 1) has a negligible weight and a coefficient of static friction μ = 0.5 with all contacting surfaces. Figure NO < 1 of 1 Part A Determine the angle so that it is self-locking. This requires no slipping for any magnitude of the force P applied to the joint. Express your answer in degrees to three significant figures. 0= Submit VE ΑΣΦ | 1 Provide Feedback Request Answer vec ?
The wedge in (Figure 1) has a negligible weight and a coefficient of static friction μ = 0.5 with all contacting surfaces. Figure NO < 1 of 1 Part A Determine the angle so that it is self-locking. This requires no slipping for any magnitude of the force P applied to the joint. Express your answer in degrees to three significant figures. 0= Submit VE ΑΣΦ | 1 Provide Feedback Request Answer vec ?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Can iu explain the geometry behind this problem. Step my step please.
![### Wedge Mechanics Problem
The wedge in **Figure 1** is designed with negligible weight and features a coefficient of static friction \( \mu_s = 0.5 \) across all contact surfaces.
#### Task
**Part A**
Determine the angle \( \theta \) so that the wedge is self-locking. This condition ensures that no slipping occurs, irrespective of the magnitude of the force \( P \) applied to the joint.
**Instructions:**
Express your answer in degrees to three significant figures.
\[ \theta = \, \]
**Submit Your Answer**
---
### Diagram Analysis
The diagram shows a wedge being pushed by two forces \( P \), directed towards the center, with an angle \( \theta/2 \) between the wedge surfaces and the horizontal plane on each side. The wedge's geometry is symmetrical, and friction is present due to the coefficient of static friction, influencing self-locking conditions.
**Note:** Students should consider the effects of friction and geometry in calculating the angle \( \theta \) that achieves self-locking.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66f4da1e-847b-4b88-b6c9-6c1db3829f53%2F5488188f-80d8-4c6e-821d-eab326f3ed72%2Fr27gezt_processed.png&w=3840&q=75)
Transcribed Image Text:### Wedge Mechanics Problem
The wedge in **Figure 1** is designed with negligible weight and features a coefficient of static friction \( \mu_s = 0.5 \) across all contact surfaces.
#### Task
**Part A**
Determine the angle \( \theta \) so that the wedge is self-locking. This condition ensures that no slipping occurs, irrespective of the magnitude of the force \( P \) applied to the joint.
**Instructions:**
Express your answer in degrees to three significant figures.
\[ \theta = \, \]
**Submit Your Answer**
---
### Diagram Analysis
The diagram shows a wedge being pushed by two forces \( P \), directed towards the center, with an angle \( \theta/2 \) between the wedge surfaces and the horizontal plane on each side. The wedge's geometry is symmetrical, and friction is present due to the coefficient of static friction, influencing self-locking conditions.
**Note:** Students should consider the effects of friction and geometry in calculating the angle \( \theta \) that achieves self-locking.
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