A 1.2-m plank with a mass of 3 kg rests on two joists. Knowing that the coefficient of static friction between the plank and the joists is 0.30, determine the magnitude of the horizontal force required to move the plank when (a) a = 750 mm, (b) a = 900 mm.
Fig. P8.37
(a)
Find the magnitude of the horizontal force required to move the plank.
Answer to Problem 8.37P
The magnitude of the horizontal force required to move the plank is
Explanation of Solution
Given information:
The length of the plank is
The mass of each plank is
The coefficient of static friction between the plank and the joists is
The distance between the points A and C in the plank is
Calculation:
Find the friction force (F) using the relation.
Show the free-body diagram of the member AB is vertical plane as in Figure 1.
Take moment about point A.
Resolve the vertical component of forces.
Show the free-body diagram of the member AB is horizontal plane as in Figure 2.
Take moment about point A.
Resolve the vertical component of forces.
Find the weight of the plank (W) using the relation.
Here, the acceleration due to gravity is g.
Consider the acceleration due to gravity is
Substitute 3 kg for m and
Substitute 29.43 N for W, 1.2 m for L, and 750 mm for a in Equation (1).
Substitute 29.43 N for W, 1.2 m for L, and 750 mm for a in Equation (2).
Substitute 1.2 m for L, and 750 mm for a in Equation (3).
Substitute 1.2 m for L, and 750 mm for a in Equation (4).
At point A, the plank to slip;
Find the horizontal force P using the relation.
Substitute 0.6P for
At point C, the plank to slip;
Find the horizontal force P using the relation.
Substitute 1.6P for
The smallest value of P will slip the plank. The plank will slip at A.
Therefore, the magnitude of the horizontal force required is
(b)
Find the magnitude of the horizontal force required to move the plank.
Answer to Problem 8.37P
The magnitude of the horizontal force required is
Explanation of Solution
Given information:
The length of the plank is
The mass of each plank is
The coefficient of static friction between the plank and the joists is
The distance between the points A and C in the plank is
Calculation:
Refer part (a) for calculation.
Substitute 29.43 N for W, 1.2 m for L, and 900 mm for a in Equation (1).
Substitute 29.43 N for W, 1.2 m for L, and 900 mm for a in Equation (2).
Substitute 1.2 m for L, and 900 mm for a in Equation (3).
Substitute 1.2 m for L, and 900 mm for a in Equation (4).
At point A, the plank to slip;
Find the horizontal force P using the relation.
Substitute 0.3333P for
At point C, the plank to slip;
Find the horizontal force P using the relation.
Substitute 1.3333P for
The smallest value of P will slip the plank. The plank will slip at C.
Therefore, the magnitude of the horizontal force required is
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Chapter 8 Solutions
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