one at each end, A 350N bucket of bolts is located 2.5m from the left end of the scaffold, and a 950N worker is standing 3.25m from the right end of the scaffold. What are the forces acting on the two support ropes?
The total force acting on the two ropes is equal to the total weight. T1 + T2 = 200 + 350 + 950 = 1500 N Counter clockwise torque = Clockwise torque Let the pivot point be at the left end. Counter clockwise torque = T2 * 8 The weight of the scaffold is at the center. The distance from the left end to the worker = 8 – 3.25 = 4.75 m Clockwise torque = 350 * 2.5 + 200 * 4 + 950 * 4.75 = 6187.5 T2 * 8 = 6187.5 T2 = 6187.5 ÷ 8 = 773.4375 N T1= 1500 – 773.4375 = 726.5625 N 0 …… 3.25 … 4.00 .… 4.75 ……… 8.00 T1↑ …350↓ … 200↓ … 950↓ ……… T12↑ I hope this helps you understand how to solve this type of problem!
Okay so we can tell that each rope supports 100N of the scaffold. Now for each mass, we can simply use the ratio of how far it is from one end to the total length to get the force on each rope. For example, if the mass was exactly in the middle, both ropes would have the same force acting on them. So, 2.5/8 * 350 [N] = 109.375 [N] 5.5/8 * 350 [N] = 240.625 [N] And, 3.25/8 * 950 [N] = 385.9375 [N] 4.75/8 * 950 [N] = 564.0625 [N] So the force on the left rope is F = 100 [N] + 240.625 [N] + 385.9375 [N] = 726.5625 [N] Force on left rope = 730 [N] (2 sig figs) F = 100 [N] +109.375 [N] + 564.0625 [N] = 774.4375 [N] Force on the right rope = 770 [N] (2 sig figs) If you're confused which forces to add, just remember that the rope feels more force as you get closer to it. Always remember to check your answer, in this case it makes sense that the rope on the right feels more force, since the heavier object is closer to it. In addition, we can also sum the forces 200 [N] + 350 [N] + 950 [N] = 1500 [N] = 730 [N] + 770 [N] Which checks out!
