Answer:
A) T2 = 912.88 N
B) T1 = 607.12 N
Explanation:
First of all, we see that the sum of the tensions is equal to the total weight.
Now, for the scaffold, weight; W_s = 77 x 9.8 = 755.6 N
For the window washer, Weight; W_w = 78 x 9.8 = 764.4 N
Total weight;W_t = W_s + W_w
W_t = 755.6 N + 764.4 N = 1520 N
Thus,
T1 + T2 = 1520
Where T1 and T2 are the tensions in farther and nearer cables respectively.
Now, we need to do a torque problem.
The window washer is 1.8m from the right end of the scaffold and so the weight of the scaffold is at its center. This is 2.5 m from either end. Let the pivot point be at right end of the scaffold.
For the window washer, counter clockwise torque = 764.4 x 1.5 = 1146.6 N.m
For the scaffold, counter clockwise torque = 755.6 x 2.5 = 1889 N.m
Total Torque; T = 1146.6 + 1889 = 3035.6 N.m
For the cable at the left end of the cable, clockwise torque = T1 x 5
Set this equal to the total counter clockwise torque and solve for T1.
Thus,
T1 x 5 = 3035.6
T1 = 3035.6 ÷ 5 = 607.12 N
T2 = 1520 – 607.12 = 912.88 N
