Concept explainers
PROBLEM 4.117
A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cable DCE that passes over n frictionless hook at C. Assuming that the tension is the same in both parts of the cable, determine (a) the tension in the cable, (b) the reactions at A and B. Assume that the hinge at B does not exert any axial thrust.
(a)
The tension on the cable.
Answer to Problem 4.117P
The tension on the cable is
Explanation of Solution
The tension in the cable
Figure 1
The position vector of the point
The position vector of the point
The position vector of the point
The vector
The tension across the cable from
Here,
Substitute
The tension across the cable from
Here,
Substitute
The weight is given as,
Here,
Substitute
The force on the point is zero. This means that the sum of the moments of the force will also be zero.
Here,
Substitute the vector values and determine the cross product.
Conclusion:
Equate the coefficients of
Therefore, the tension on the cable is
(b)
The reactions at
Answer to Problem 4.117P
The reactions at
Explanation of Solution
The free body diagram of the given arrangement is given in Figure 1.
Equate the coefficients of
Equate the coefficients of
The net force acting on the point is zero.
Here,
Substitute
Equate the coefficients of
Equate the coefficients of
Equate the coefficients of
Conclusion:
From (II) and (III) the vector
And, from (V), (VI) and (VII) the vector
Therefore, the reactions at
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