Calculating Tension of Rope for Scaffold with 690N Worker

[esinn08]

Hi everyone,

My question is as follows:

A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 190N and is 2.9m long. What is the tension in each rope when the 690N worker stands 1.9m from one end?

I know the sum of the forces has to be 0, since the scaffold isn't moving. I also know to get the tension you multiply the weight by the appropriate length. I'm just not sure where to go from there. Any suggestions would be greatly appreciated

Thanks for your help!

 

[PhanthomJay]

Hi everyone,

My question is as follows:

A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 190N and is 2.9m long. What is the tension in each rope when the 690N worker stands 1.9m from one end?

I know the sum of the forces has to be 0, since the scaffold isn't moving. I also know to get the tension you multiply the weight by the appropriate length. I'm just not sure where to go from there. Any suggestions would be greatly appreciated

Thanks for your help!

The sum of the forces AND the sum of the torques must equal zero. The scaffold weight may be represented by a single 190N force acting 1.45m from one end (that is, in the middle). The tension forces are unknown at this point, call them T_1 and T_2 (they will act UP). By summing torques (force times perpendicular distance) about one end, and setting them equal to zero, watching your plus and minus signs (clockwise is plus and counterclockwise is minus), you can solve for one of the tension forces, and then the other by noting sum of all forces in vertical direction is 0.

 

[esinn08]

(I made a typo in my question, the scaffold is 690N and the person is 190N.)

Regardless, I am not sure that I am completely understanding what you wrote.

(1.45m)(-690N) + (T_1)(1.45m) = 0

(1.9m)(-190N) + (T_2)(1.0m) = 0

I have a feeling that is not right. Any more suggestions?