Concept explainers
(a) Show that the beam of Prob. 8.41 cannot be moved if the top surface of the dolly is slightly lower than the platform. (b) Show that the beam can be moved if two 175-lb workers stand on the beam at B, and determine how far to the left the beam can be moved.
8.41 A 10-ft beam, weighing 1200 lb, is to be moved to the left onto the platform as shown. A horizontal force P is applied to the dolly, which is mounted on frictionless wheels. The coefficients of friction between all surfaces are μs = 0.30 and μs = 0.25, and initially, χ = 2 ft. Knowing that the top surface of the dolly is slightly higher than the platform, determine the force P required to start moving the beam. (Hint: The beam is supported at A and D.)
Fig. P8.41
(a)
Show that the beam cannot be moved if the top surface of the dolly is slightly lower than the platform.
Explanation of Solution
Given information:
The length of the beam is 10 ft.
The weight of the beam is
The coefficient of static friction between the surfaces is
The coefficient of kinetic friction between the surfaces is
Calculation:
Show the free-body diagram of the beam AB as in Figure 1.
Find the normal force at point B by taking moment about end C.
Find the normal force at point C by resolving the vertical component of forces.
Find the maximum friction force at point C
Substitute 0.30 for
Find the maximum friction force at point B
Substitute 0.30 for
The maximum friction force at point B is less than the maximum friction force at point C.
The sliding is about to happen at point B.
Therefore, the beam
(b)
Show that the beam can be moved if two 175-lb workers stand on the beam at B.
Find the distance the beam moves to the left.
Answer to Problem 8.42P
The distance the beam moves to the left is
Explanation of Solution
Given information:
The length of the beam is 10 ft.
The weight of the beam is
The coefficient of static friction between the surfaces is
The coefficient of kinetic friction between the surfaces is
Calculation:
Show the free-body diagram of the beam AB as in Figure 2.
Find the normal force at point B by taking moment about end C.
Find the normal reaction at point C by taking moment about point B.
When two 175 lb workers stand on the end B:
Substitute 2 ft for x in Equation (1).
Substitute 2 ft for x in Equation (2).
Find the maximum friction force at point C
Substitute 0.30 for
Find the maximum friction force at point B
Substitute 0.30 for
The maximum friction force at point B is greater than the maximum friction force at point C.
The sliding is about to happen at point C.
Therefore, the beam
The beam will stop moving when the friction force at point C is equal to the maximum friction force at point B.
Find the friction force at point C
Substitute 0.25 for
Find the maximum friction force at point B
Substitute 0.30 for
Substitute
Therefore, the distance the beam moves to the left is
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