The document summarizes calculations to determine forces in a cable-strut system. It defines key angles between components as 15 and 45 degrees. It uses the torque equation about the hinge to find the torque T as 6.63x103 N by canceling the unknown boom length. Horizontal force Fx is then calculated as 5.74x103 N using T and the 30 degree cable angle. Vertical force Fy is calculated as 5.96x103 N using torque T, weights and gravity.

1. 25. (a) We note that the angle θ between the cable and the strut is 45◦ − 30◦ = 15◦ . The angle φ between
the strut and any vertical force (like the weights in the problem) is 90◦ − 45◦ = 45◦ . Denoting
M = 225 kg and m = 45.0 kg, and as the length of the boom, we compute torques about the
hinge and find
M g sin φ + mg 2 sin φ
T = .
sin θ
The unknown length cancels out and we obtain T = 6.63 × 103 N.
(b) Since the cable is at 30◦ from horizontal, then horizontal equilibrium of forces requires that the
horizontal hinge force be
Fx = T cos 30◦ = 5.74 × 103 N .
(c) And vertical equilibrium of forces gives the vertical hinge force component:
Fy = M g + mg + T sin 30◦ = 5.96 × 103 N .