2020-12-10T08:27:34-05:00
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.
1
2020-12-21T11:04:47-0500
l 1 cos a = l 2 cos b = l 2 cos ( 90 − a ) = l 2 sin a a = arctan 30 50 = 31 ° T 1 sin 31 = T 2 cos 31 T 1 cos 31 + T 2 sin 31 = m g = 2 ( 10 ) T 1 cos 31 + T 1 sin 2 31 cos 31 = 20 T 1 = 17.1 N 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 l 1 cos a = l 2 cos b = l 2 cos ( 90 − a ) = l 2 sin a a = arctan 50 30 = 31° T 1 sin 31 = T 2 cos 31 T 1 cos 31 + T 2 sin 31 = m g = 2 ( 10 ) T 1 cos 31 + T 1 cos 31 sin 2 31 = 20 T 1 = 17.1 N
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