Two 8-kg blocks A and B resting on shelves are connected by a rod of negligible mass. Knowing that the magnitude of a horizontal force P applied at C is slowly increased from zero, determine the value of P for which motion occurs and what that motion is when the coefficient of static friction between all surfaces is (a) μs = 0.40, (b) μs = 0.50.
Fig. P8.43
(a)
Find the magnitude of horizontal force P applied at C for which the motion occurs.
Answer to Problem 8.43P
The magnitude of the horizontal force P is
The system
Explanation of Solution
Given information:
The mass of the blocks A and B is
The coefficient of static friction between the surfaces is
Calculation:
Consider the blocks will slide to the right.
Find the weight (W) of the blocks A and B using the relation.
Here, the acceleration due to gravity is g.
Consider the acceleration due to gravity is
Substitute 8 kg for m and
Find the friction force at block A and B as follows.
Here, the normal force at block A is
Show the free-body diagram of the shelves as in Figure 1.
Resolve the vertical component of forces.
Resolve the horizontal component of forces.
Substitute 0.40 for
Therefore, the magnitude of the horizontal force P is
Take moment about point B.
Substitute 62.8 N for P and 0.40 for
Therefore, the system
(b)
Find the magnitude of horizontal force P applied at C for which the motion occurs.
Answer to Problem 8.43P
The
The magnitude of the horizontal force P is
Explanation of Solution
Given information:
The mass of the blocks A and B is
The coefficient of static friction between the surfaces is
Calculation:
Consider the blocks will slide to the right.
Find the weight (W) of the blocks A and B using the relation.
Here, the acceleration due to gravity is g.
Consider the acceleration due to gravity is
Substitute 8 kg for m and
Find the friction force at block A and B as follows.
Here, the normal force at block A is
Resolve the vertical component of forces.
Resolve the horizontal component of forces.
Substitute 0.50 for
Therefore, the magnitude of the horizontal force P is
Take moment about point B.
Substitute 78.48 N for P and 0.50 for
Therefore, the
The value of
Take moment about point B.
Substitute 0 for
Therefore, the magnitude of the horizontal force P is
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Chapter 8 Solutions
Vector Mechanics for Engineers: Statics
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