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
Want to see more full solutions like this?
Chapter 7 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
- The 60-lb plank rests on a frictionless roller at A, and the 20-lb triangular support BD. Both bodies are homogenous. The coefficients of static friction are 0.4 at B and 0.3 at D. Determine the largest force P that can be applied to the plank without initiating motion.arrow_forwardThe blocks A and B of weights WA and WB are joined by a rope that passes over the fixed peg C. The coefficients of static friction are =0.2 between block A and the inclined plane, and =0.25 between the rope and the peg. Determine the range of Wb/WA for which the system will be in equilibrium.arrow_forwardThe uniform bar of weight W is supported by a ball-and-socket joint at A and rests against a vertical wall at B. If sliding impends when the bar is in the position shown, determine the static coefficient of friction at B. [Hint The direction of impending sliding is tangent to the dashed circle (the potential path of motion of point B).]arrow_forward
- The 320-lb homogeneous spool is placed on the inclined surface. Determine the vertical force P that is required to keep the spool in the position shown. Assume that there is enough friction to prevent slipping at A.arrow_forwardFind the largest value of b/h at which the folding table is in equilibrium. The coefficients of static friction are 0.5 at A and 0.3 at C. Neglect the weight of the table.arrow_forwardThe two homogeneous bars AB and BC are connected with a pin at B and placed between rough vertical walls. If the coefficient of static friction between each bar and the wall is 0.25, determine the largest angle 6 for which the assembly will remain at rest.arrow_forward
- The coeffient of static friction between the uniform bar AB of weight W and the ground is 0.45. Find the smallest angle and the corresponding force P that would initiate simultaneous tipping and sliding of the bar.arrow_forwardThe mass of the unbalanced disk is m, and its center of gravity is located at G. If the coefficient of static friction is 0.2 between the cylinder and the inclined surface, determine whether the cylinder can be at rest in the position shown. Note that the string AB is parallel to the incline.arrow_forwardThe 3600-lb car with rear Wheel drive is attempting to tow the 4500-lb crate. The center of gravity of the car is at G, and the coefficients of static friction are 0.6 at B and 0.2 at C. Determine if the crate will slide.arrow_forward
- A 1.1-kg disk A is placed on the inclined surface. The coefficient of static friction between the disk and the surface is 0.35. Is the disk in equilibrium if P=5.5N and =30?arrow_forwardFind the smallest distance d for which the hook will remain at rest when acted on by the force P. Neglect the weight of the hook, and assume that the vertical wall is frictionless.arrow_forwardThe cone clutch transmits the torque C through a conical friction surface with cone angle . The inner and outer radii of the friction surface are a and b, respectively. The left half of the clutch is keyed to the shaft, and the right half drives a machine (not shown) through a gear attached to its outer rim. Assuming uniform pressure on the friction surface, show that the maximum torque that can be transmitted by the clutch isarrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L