Question

A rope 11m long is fastened to two hooks 9m apart on a horizontal ceiling. To the rope is attached a 400n weight so that the segments of the rope are 7m and 4m. Determine the tension in each segment.

Answer 1

$$T_1sinα = T_2sinβ\\T_1\frac{h}{7} = T_2\frac{h}{4}\\T_1=1.75T_2$$

$$T_1cosα + T_2cosβ = W\\1.75T_2\cos{48} + T_2\cos{25}= 400$$

$$T_2=193\ N\\T_1=337\ N$$