A 15° wedge is forced under a 50-kg pipe as shown. Knowing that the coefficient of static friction at both surfaces of the wedge is 0.20, determine the largest coefficient of static friction between the pipe and the vertical wall for which slipping will occur at A.
Fig. P8.64 and P8.65
Find the largest coefficient of static friction between the pipe and the vertical wall for the condition.
Answer to Problem 8.65P
The largest coefficient of static friction between the pipe and the vertical wall is
Explanation of Solution
Given information:
The mass of the pipe is
The value of angle
The coefficient of static friction at all surfaces is
Calculation:
Find the weight (W) of the pipe using the relation.
Here, the acceleration due to gravity is g.
Consider the acceleration due to gravity is
Substitute 50 kg for m and
Show the free-body diagram of the pipe as in Figure 1.
Find the friction force at point B using the relation.
Here, the normal force at point B is
Find the normal force at point B by taking moment about point A.
Substitute 490.5 N for W, 0.20 for
Find the normal force at point A
Substitute 0.20 for
Find the friction force at point A
Substitute 490.5 N for W, 0.20 for
Find the coefficient of static friction at point A
Substitute 137.507 N for
Therefore, the largest coefficient of static friction between the pipe and the vertical wall is
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Chapter 8 Solutions
Vector Mechanics for Engineers: Statics
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