Finding Tension in Scaffolding

[Dante5454]

[SOLVED] Finding Tension in Scaffolding

Homework Statement

A 656N window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 171N and is 4.58m long. Assume the window washer stands 1.33m from the left end. What is the tension in both ropes. (Answer in N)

Homework Equations

Static Equilibrium States $$\Sigma$$Torques=0 also $$\Sigma$$Forces=0

The Attempt at a Solution

I first solved for the center of gravity, using the left end as a datum using the equation (sum of moments)/(sum of masses) = center of gravity. Then, using my new point as the lever arm for the board's weight, I solved for torque in the downward direction and thought that tension should have to be equal. I am doing this as a part of an online course, and submitted my answer, which was incorrect. I could really use help, thanks.

 

[mgb_phys]

First get the force due to the scaffold itself. This is the obvious case with nobody on it - divide that equally between the two ropes.
Now work out the total force due to the person - obviously this weight must be added to the force on the ropes, but divided between them in some ratio.

Consider what the force on each rope would be if the person was standing 1, directly under the other rope, 2, in the centre of the platform ?

You don't have to actaully work out the moments - the ratio should be obvious.

 

[Dante5454]

Perfect! Thanks so much, mgb! I just took half of the force of the scaffold, 85.5 and added it to (1.33/4.58) for the left side, and added it to (3.25/4.58) for the right side. It worked perfectly! Thanks again!