A 15° wedge is forced under a 50-kg pipe as shown. The coefficient of static friction at all surfaces is 0.20. (a) Show that slipping will occur between the pipe and the vertical wall. (b) Determine the force P required to move the wedge.
Fig. P8.64 and P8.65
(a)
Show that the slipping will occur between the pipe and the vertical wall.
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 A using the relation.
Here, the normal force at point A is
Find the normal force at point A by taking moment about point B.
Substitute 490.5 N for W, 0.20 for
Find the friction force at point B
Substitute 490.5 N for W, 0.20 for
Find the normal force at point B
Substitute 490.5 N for W, 0.20 for
Find the maximum friction force at point B using the relation.
Substitute 0.20 for
The friction force at point B is less than the maximum friction force at point B.
Therefore, the slipping will not occur at point B and the slipping will occur between the pipe and the vertical wall.
(b)
Find the force P required to move the wedge.
Answer to Problem 8.64P
The force P required to move the wedge 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:
Show the free-body diagram of the wedge as in Figure 2.
Find the normal force
Substitute 554.155 N for
Find the force P by resolving the horizontal component of forces.
Substitute 554.155 N for
Therefore, the force P required to move the wedge is
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Chapter 8 Solutions
Vector Mechanics for Engineers: Statics
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