An 800N billboard worker stands on a 4m scaffold weighing 500N and supported by vertical ropes at each end. How far would the worker stand from one of the supporting ropes to produce a tension of 550N in that rope?
a. 1.4m
b. 2m
c. 2.5m
d. 2.7m
e. 3m

Question

An 800N billboard worker stands on a 4m scaffold weighing 500N and supported by vertical ropes at each end. How far would the worker stand from one of the supporting ropes to produce a tension of 550N in that rope?
a. 1.4m
b. 2m
c. 2.5m
d. 2.7m
e. 3m

compphysgeek · Answer

OK, if free the scaffold would rotate around an axis in the middle of the board. Scaffold and worker together weigh 800N + 500N = 1300N. If the worker stood in the middle, tension in both ropes would be 650 N. When the worker moves a distance x away from the centre of the board the torque he's creating will be T = x . 800 N. For the board to stay horizontal the sum of all torques has to be 0. 

Let $T_1 = 2 \times 550 N, T_2 = -1 \times 250N, T_w = x \times 800N, T3 = 1 \times 250 N $ and $T4 = -2 \times 750N $. The sign of the torque tell us in which direction it would rotate the board if it was the only torque.

$$T_1 + T_2 + T_w + T_3 + T_4 = 0  \
1100 N - 250 N + 800 N \times x  + 250 N - 1500 N = 0$$

Solve for x. Answer c should be right.

|dw:1383734059272:dw|