A uniform plank is supported by a fixed support at A and a drum at B that rotates clockwise. The coefficients of static and kinetic friction for the two points of contact are as shown. Determine whether the plank moves from the position shown if (a) the plank is placed in position before the drum is set in motion; and (b) the plank is first placed on the support at A and then lowered onto the drum, which is already rotating.
(a)
Whether the plank moves from the position if the plank is placed in position before the drum is set in motion
Answer to Problem 7.24P
The co-efficient of friction
Explanation of Solution
Given information:
A is fixed support.
Drum rotates at clockwise.
If there is no relative motion between two surfaces that are in contact, the relationship between normal force
Steps to follow in the equilibrium analysis of a body are:
1. Draw the free body diagram.
2. Write the equilibrium equations.
3. Solve the equations for the unknowns.
Calculation:
FBD of plank
Assume
Assume
For the equilibrium of plank, the bending moment about point A is equal to zero.
Write equilibrium equation in horizontal direction.
Write equilibrium equation in vertical direction.
The plank to remain at rest, it must resist the maximum static friction force
Assume
Therefore
The co-efficient of static friction
Therefore, the plank will slide at point A.
Conclusion:
The co-efficient of friction
(b)
Whether the plank moves from the position if the plank is first placed on support A and then lowered onto the drum
Answer to Problem 7.24P
The co-efficient of friction
Explanation of Solution
Given information:
A is fixed support.
Drum rotates at clockwise.
If there is no relative motion between two surfaces that are in contact, the relationship between normal force
Steps to follow in the equilibrium analysis of a body are:
1. Draw the free body diagram.
2. Write the equilibrium equations.
3. Solve the equations for the unknowns.
Calculation:
According to sub part a
The plank to remain at rest, it must slip on the drum at point B.
Therefore
The co-efficient of static friction
Therefore, the plank will not move.
Conclusion:
The co-efficient of friction
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Chapter 7 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L