A 15-ft beam weighing 500 Ib is lowered by mean of two cables unwinding from overhead cranes. As the beam approaches the ground, the crane operators apply brakes to slow the unwinding motion. Knowing that the deceleration of cable A is 20 ft/s2 and the deceleration of cable B is 2 ft/s2, determine the tension in each cable.
The tension in each cable.
Answer to Problem 16.60P
The tension in cable
The tension in cable
Explanation of Solution
Given information:
The length of the beam is
The below figure represent the kinetics of the beam.
Figure-(1)
Write the expression of total force applied on the beam.
Here, the mass of the beam is
Consider the tension in the cable
Write the expression of deceleration of cable
Here, the acceleration of cable
Write the expression of total acceleration on the beam.
Here, the acceleration of the cable
Write the expression of moment of inertia of beam.
Here, the mass of the slender rod is
Write the expression of mass of the rod.
Here, the weight of the beam is
Write the expression of total moment about point
Here, the effective moment is
Write the expression of moment about point
Here, the tension in the cable
Write the expression of effective moment about point
Here, the angular acceleration of the rod is
Write the expression of generated torque in the beam.
Here, the of inertia of beam is
Substitute
Substitute
Substitute
Write the expression of total force applied on the beam by equilibrium of the beam as shown in Figure-(1).
Substitute
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The tension in cable
The tension in cable
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Chapter 16 Solutions
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