Concept explainers
The ladder AB, of length L and weight W, can be raised by BC. Determine the tension T required to raise end B just off floor (a) in terms of W and θ, (b) if h = 8 ft, L = 10 ft, and W = lb.
Fig. P4.21
(a)
The tension in the cable AB shown in figure
Answer to Problem 4.20P
The tension in the cable AB shown in figure
Explanation of Solution
Forces acting upward and rightward are considered as positive and the torque acting counter clockwise is considered as positive.
The free body diagram is sketched below as figure 1.
Here,
Write the expression for the moment at
Here,
The moment at
Thus, the complete expression of
Here,
At equilibrium, the sum of the moment acting at
Write the expression for the ration of
Write the expression for
Write the expression for the magnitude of tension in the cable
Here,
Calculation:
Rearrange equation (III) to get
Substitute
Substitute
Substitute
Therefore, the tension in the cable AB shown in figure
(b)
The reaction at
Answer to Problem 4.20P
The reaction at
Explanation of Solution
Write the expression for the net force along the
Here,
The negative sign for
At equilibrium, the net force along the
Write the expression for the net force along the
Except the force
Here,
At equilibrium, the net force along the
Write the expression for the magnitude of reaction at
Here,
Calculation:
Substitute
Substitute
Substitute
Let
Therefore, the tension in the cable AB shown in figure
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Chapter 4 Solutions
Vector Mechanics for Engineers: Statics, 11th Edition
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