Question

a 90 kg architect is standing 2 meters from the center of a scaffold help up by a rope on both sides. the scaffold is 6m long and has a mass of 200kg. what is the tension on each rope

Answer 1

We can solve the problem by requiring the equilibrium of the forces and the equilibrium of torques.

1) Equilibrium of forces:

`T_1 - W_p - W_s + T_2 =0`
where

`W_p = (90kg)(9.81 m/s^2)=883 N` is the weight of the person

`W_s = (200kg)(9.81 m/s^2)=1962 N` is the weight of the scaffold
Re-arranging, we can write the equation as

`T_1 = 2845 N-T_2` (1)

2) Equilibrium of torques:

`T_1 \cdot 3 m - W_p \cdot 2 m - T_2 \cdot 3m =0`
where 3 m and 2 m are the distances of the forces from the center of mass of the scaffold.
Using
`W_p = 883 N` and replacing T1 with (1), we find

`2845 N \cdot 3 m - T_2 \cdot 3 m - 833 N \cdot 2 m - T_2 \cdot 3 m=0`
from which we find

`T_2 = 1128 N`

And then, substituting T2 into (1), we find

`T_1 = 1717 N`