Static Equilibrium

Q. Static Equilibrium

Question                                     

The 50kg mass is supported by a five cable system as shown inthe figure.

Determine the tension in all cables.

Answer

For equilibrium of C in the vertical direction,
Tcd sin30° = 50 * 9.81
=> Tcd = 981 N

For equilibrium of BC,
Tbc 
= Tcd cos30°
= 981 * cos30°
= 849.6 N

For equilibrium of B in the vertical direction,
Tab sin45° - Tbe sin30° = 0 ... (1)
For equilibrium of B in the horizontal direction,
Tabcos45° + Tbe cos30° = Tbc = 849.6 ... (2)

Subtracting (2) from (1),
Tbe (cos30° + sin30°) = 849.6
=> Tbe = 622 N

Plugging Tbe in eqn. (1),
Tab 
= Tbe (sin30°/sin45°)
= 622 * (sin30°/sin45°)
= 439.8 N.

Tcf = 50 * 9.81 = 490.5 N.

Answers: 
Tab = 439.8N, 
Tbc = 849.6N, 
Tbe = 622N, 
Tcd = 981N, 
Tcf = 490.5N