A 1-ton load (2,000 pounds) is supported by two cables, making angles with the h

Question

A 1-ton load (2,000 pounds) is supported by two cables, making angles with the horizontal, respectively, equal to 60degree and 30degree as shown in Fig. 2. Determine the tension in the two cables, i.e., determine the magnitude of the forces F_1 and F_2. In the figure, the weight is illustrated with the force vector F_3. (a) |F_1| 1724 lbs.; |F_2| 1000 lbs. (b) |F_1| 1000 lbs.; |F_2| 724 lbs. (c) |F_1| 1233 lbs.; |F_2| 1105 lbs. (d) |F_1| 1847 lbs.; |F_2| 1236 lbs. (e) |F_1| 1236 lbs.; |F_2| 1747 lbs.

Explanation / Answer

Balancing forces,

F1cos(60) = F2cos(30)

F1 = 3 *F2 --------------------(1)

F1sin(60) + F2sin(30) = 2000

3*F2/2 + F2/2 = 2000

F2 = 1000 lbs

F1 = 3 *F2 = 3 *1000 = 1724 lbs

So answer is (a)

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