Answer to Question #150286 in Physics for Kamran

Question

A load weighing 2 kg hangs on two light ropes of 30 cm and 50 cm. The ropes are attached to the horizontal ceiling, the angle between the ropes is 90°. Find the pulling force of the short rope. Take g = 10 m/s^2.

Answer 1

$$l_1\cos{a}=l_2 \cos{b}=l_2 \cos{(90-a)}=l_2 \sin{a}\\a=\arctan{\frac{30}{50}}=31\degree\\ T_1\sin{31}=T_2\cos{31}\\T_1\cos{31}+T_2\sin{31}=mg=2(10)\\ \\T_1\cos{31}+T_1\frac{\sin^2{31}}{\cos{31}}=20\\T_1=17.1\ N$$