21. A traffic signal of mass 25.0 kg is suspended by two cables as shown in the diagram below. Solve for the tension in each cable each of the following scenarios: (a) θ1 = θ2 = 20.0°, and (b) θ1 = 20.0°, θ2 = 30.0°.

Answer 1

M*g = 25 * 9.8 = 235 N. = Wt. of signal.

a. Given: A1 = A2=20o. Therefore,T1=T2.
-235i + T1*sin(180-20) + T2*sin20 = 0.
Replace T2 with T1:
-235i + T1*sin(180-20) + T1*sin20 = 0.
0.342T1 + 0.342T1 = 235i.
0.684i*T1 = 235i.
T1 = 344N. = T2.

b. T1*Cos(180-20) + T2*Cos30 = 0.
-0.940T1 + 0.866T2 = 0.
T2 = 1.09T1.

T1*sin(180-20) + T2*sin30 = -(-235i).
Replace T2 with 1.09T1:
0.342i*T1 + 1.09T1*sin30 = 235i.
0.342i*T1 * 0.545i*T1 = 235i.
0.887i*T1 = 235i.
T1 = 265 N.
T2 = 1.09*265 = 289 N.