Question

A perfectly flexible and inextensible cable is shown in the figure (not to scale). The external loads at F and G are acting vertically. 

Hint:

For a flexible and inextensible cable, the tension is determined by the vertical loads acting on the cable.

Answer 1

Correct Answer: 8.1

The tension in the cable segment \( FG \) can be calculated using the equilibrium conditions for the forces acting on the cable. The external loads \( P_F = 10 \, \text{kN} \) and \( P_G = 12 \, \text{kN} \) create a triangular shape in the cable. The total vertical load acting on the segment \( FG \) is the sum of the loads at \( F \) and \( G \), which is: \[ P_{\text{total}} = P_F + P_G = 10 \, \text{kN} + 12 \, \text{kN} = 22 \, \text{kN}. \] Since the cable is perfectly flexible, the tension in the cable segment is equal to the vertical load at \( G \), which is \( 10 \, \text{kN} \). Thus, the tension in the cable segment \( FG \) is \( \boxed{10} \, \text{kN} \).