A 666 N window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 396 N and is 3.72 m long. Assume the window washer stands 1.2 m from the left end. What is the tension in the rope on the right?
396 x (.5 x 3.72) = 736.56N/m. 666 x 1.2 = 799.2N/m. (799.2 + 736.56)/3.72 = tension of 412.84N. in the right rope.
Do a moment balance about the left end. Sum of the moments about the left end = 0 (CCW is +)... Basically the weights want to spin the scaffold in the clockwise direction and the tension wants to sping the scaffold in the counterclockwise direction. 0 = -666 N * 1.2 m - 396 N * 3.72 m / 2 + T*3.72 m Solve for T T = 413 N
This is torque problem. Let the pivot point be at the left end. The weight of the scaffold is at its center. ? * 3.72 = 1.86 meters This is the distance from the left end. The weights of the window washer and scaffold will produce clockwise torque. The tension in the on the right will produce counter clockwise torque. For the window washer, torque = 666 * 1.2 = 799.2 For the scaffold, torque = 396 * 1.86 = 736.56 Total = 799.2 + 736.56 = 1535.76 For the rope, torque = T * 3.72 T * 3.72 = 1535.76 T = 1535.76 ÷ 3.72 The tension is approximately 412.84 N
