Concept explainers
Fig. P4.89
4.90 Knowing that for the rod of Prob. 4.89, L = 15 in., R = 20 in., and W = 10 lb, determine (a) the angle θ corresponding to equilibrium, (b) the reactions at A and B.
(a)
The angle
Answer to Problem 4.90P
The angle
Explanation of Solution
The free-body diagram corresponding to the arrangement in Fig. P4.89 is given in Figure 1. The reaction at
Write the expression for the distances
Write the expression for the distances
Write the expression of Pythagoras theorem in the triangle
Conclusion:
Use equation (I) and (II) in (III).
Use equation (IV), (V) and (VII) in (VI).
Simplify equation (VIII).
The expression for the equilibrium condition of the rod is,
Given that the length of the rod is
Substitute
Therefore, the angle
(b)
The reaction at
Answer to Problem 4.90P
The reaction at
Explanation of Solution
The free-body diagram corresponding to the arrangement is given in Figure 1.
Write the expression for computing the angle
Use equation (IV) and (VII) in (X).
At the equilibrium condition, a force triangle can be drawn using
Conclusion:
Substitute
The force triangle using
Write the trigonometric relation for determining
Write the trigonometric relation for det4ermoini ng
Substitute
and,
The reaction at
Therefore, the reaction at
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Chapter 4 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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