Cords AB and AC can each sustain a maximum tension of 800 lb. If the drum has a weight of 900 lb, determine the smallest angle θ at which they can be attached to the drum.
Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.
Solution:
Let us first draw a free body diagram showing the forces at A.
The question states that cords AB and AC can both sustain a maximum of 800 lb. In addition, note that a force of 900 lb will be carried by the cord extending upwards from A, as this cable must take the full weight of the pipe.
Let us now write an equation of equilibrium for the y-axis forces.
+\uparrow \sum \text{F}_\text{y}\,=\,0
900-800\sin\theta-800\sin\theta=0
1600\sin\theta=900
\sin\theta=\dfrac{900}{1600}
\theta=\sin^{-1}\left(\dfrac{900}{1600}\right)
\theta=34.2^0
900-800\sin\theta-800\sin\theta=0
1600\sin\theta=900
\sin\theta=\dfrac{900}{1600}
\theta=\sin^{-1}\left(\dfrac{900}{1600}\right)
\theta=34.2^0