Concept explainers
Solve Prob. 8.93 assuming that the normal force per unit area between the disk and the floor varies linearly from a maximum at the center to zero at the circumference of the disk.
8.93 A 50-lb electric floor polisher is operated on a surface for which the coefficient of kinetic friction is 0.25. Assuming that the normal force per unit area between the disk and the floor is uniformly distributed, determine the magnitude Q of the horizontal forces required to prevent motion of the machine.
Fig. P8.93
Find the magnitude Q of the horizontal force required to prevent motion of the machine.
Answer to Problem 8.97P
The magnitude Q of the horizontal force is
Explanation of Solution
Given information:
The diameter of the electric floor polisher is
The weight of the electric floor polisher is
The coefficient of kinetic friction is
Calculation:
Show the free-body diagram of the thrust bearing as in Figure 1.
It has been assumed that the normal force per unit area is inversely proportional to r.
Here, the distance between the point to the axis of the shaft is r, the change is angle is
Find the normal force exerted
Substitute
Find the value of k using the relation.
Substitute
Substitute
Find the change in friction force
Substitute
Find the change in moment
Substitute
Integrate the equation to find the couple M.
Substitute
Substitute 0.25 for
Refer to the given figure;
Resolve the moment component in y-axis as follows;
Substitute
Therefore, the magnitude Q of the horizontal force is
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Chapter 8 Solutions
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