A bucket hangs from two wires. The left-hand wire makes an angle of 60 with the vertical, and the magnitude of the tension in the wire is 326N. The right-hand wire makes an angle of 45 with the vertical.

Question

A bucket  hangs from two wires. The left-hand wire makes an angle of 60 with the vertical, and the magnitude of the tension in the wire is 326N. The right-hand wire makes an angle of 45 with the vertical.

Calculate the mass of the bucket, in kilograms,  to two significant figures.
(Take the magnitude of the acceleration due to gravity, g, to be 9.8ms^-2)

Henry · Answer

60o W. of N. = 150o CCW from +x-axis.

45o E. of N. = 45o CCW from +x-axis.

The system is in equilibrium:

326*cos150 = -T2*cos45.
326 = 0.742T2, T2 = 400 N.

Fb = -(T1*sin150+T2*sin45).
Fb = -(326*sin150+400*sin45) = -446 N. = 446 N. Downward.

M*g = 446. M = 446/g = 446/9.8 = 46 kg.

Henry · Answer

Correction: 326 = 0.816T2, T2 = 400 N.