Concept explainers
To unload a bound stack of plywood from a truck, the driver first tilts the bed of the truck and then accelerates from rest. Knowing that the coefficients of friction between the bottom sheet of plywood and the bed are μs = 0.40 and μk = 0.30, determine (a) the smallest acceleration of the truck which will cause the stack of plywood to slide, (b) the acceleration of the truck which causes corner A of the stack to reach the end of the bed in 0.9 s.
Fig. P12.22
(a)
Find the smallest acceleration of the truck which will cause the stack of plywood to slide.
Answer to Problem 12.22P
The smallest acceleration of the truck which will cause the stack of plywood to slide is
Explanation of Solution
Given information:
The coefficients of static friction
The coefficients of static friction
The tilting angle
The relative distance of plywood with respect to truck
Calculation:
Write the equation of Weight of plywood
Here,
Sketch the free body diagram and kinetic diagram of plywood as shown in Figure (1).
Refer Figure (1).
Apply the Newton’s law of equation along y-axis.
Substitute
Write the equation of friction force
Here,
Substitute 0.40 for
Substitute
Apply the Newton’s law of equation along x-axis.
Substitute
Find the smallest acceleration of the truck which will cause the stack of plywood to slide.
Equate Equation (1) and (2).
Substitute
Thus, the smallest acceleration of the truck which will cause the stack of plywood to slide is
(b)
Find the acceleration of the truck which causes corner A of the stack to reach the end of the bed in 0.9 s.
Answer to Problem 12.22P
The acceleration of the truck which causes corner A of the stack to reach the end of the bed in 0.9 s is
Explanation of Solution
Calculation:
The velocity of plywood relative to truck is zero.
Find the acceleration of the plywood relative to the truck
Here,
Substitute 0 for
Sketch the free body diagram and kinetic diagram of truck as shown in Figure (2).
Refer Figure (2).
Apply the Newton’s law of equation along y-axis.
Substitute
Here,
Apply the Newton’s law of equation along x-axis.
Substitute
Here,
Write the equation of frictional force on truck:
Substitute 0.30 for
Find the acceleration of the truck
Equate Equation (4) and (5),
Substitute
Thus, the acceleration of the truck which causes corner A of the stack to reach the end of the bed in 0.9 s is
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