Concept explainers
F8–1. Determine the friction developed between the 50-kg crate and the ground if a) P=200 N, and b) P=400 N. The coefficients of static and kinetic friction between the crate and the ground are, μs = 0.3 and, μk = 0.2.
(a)
The frictional force (F).
Answer to Problem 1FP
(a) The frictional force (F) is
(b) The frictional force (F) is
Explanation of Solution
Given:
The mass of the crate (m) is 50 kg.
The co-efficient of static friction
The co-efficient of kinetic friction
Show the free body diagram of the crate as in Figure (1).
Using Figure (1),
Determine the normal reaction (N) using the equation of equilibrium.
Along the vertical direction:
Here, the acceleration due to gravity is g.
Determine the frictional force using the equation of equilibrium.
Along the horizontal direction:
Conclusion:
Substitute 50 kg for m,
Substitute 200 N for P in Equation (II).
Check:
Determine the maximum frictional force.
Substitute 0.3 for
The maximum frictional force (183.15 N) is greater than the frictional force (160 N); therefore the block will not slip.
Therefore, the frictional force is
(b)
The frictional force (F).
Answer to Problem 1FP
The frictional force (F) is
Explanation of Solution
Given:
The mass of the crate (m) is 50 kg.
The co-efficient of static friction
The co-efficient of kinetic friction
Show the free body diagram of the crate as in Figure (2).
Using Figure (2),
Determine the normal reaction (N) using the equation of equilibrium.
Along the vertical direction:
Determine the frictional force using the equation of equilibrium.
Along the horizontal direction:
Conclusion:
Substitute 50 kg for m,
Substitute 400 N for P in Equation (IV).
Check:
Determine the maximum frictional force.
Substitute 0.3 for
The maximum frictional force (219.15 N) is less than the frictional force (320 N); therefore the block will slip. Hence, find the frictional force using the co-efficient of kinetic friction.
Find the frictional force using the relation.
Substitute 0.2 for
Thus, the frictional force is
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Chapter 8 Solutions
EBK ENGINEERING MECHANICS
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L