static equilibrium

Question

A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 300 N and is 4.50 m long. What is the tension in each rope when the 600-N worker stands 1.30 m from one end?

Make use of the situations in this scenario and tell us a story of your own that involves a similar type of static equilibrium. You may use approximate values to solve the problem that you come up with.



please label what the measurements are for the left and right-handed side ropes.*

Answer 1

(I answered this question previously.)

Because the scaffold is in static equilibrium the forces and moments must be balanced.

The vertical forces are the weight of the scaffold (300N) which acts in the center - 2.25m from either end (assuming it's homogeneous); and the weight of the window washer (600N) which acts 1.3m from one end. Tension in the two supporting ropes balance these forces, so:

The sum of vertical forces are zero:

T₁ + T₂ - 300 - 600 = 0

T₁ + T₂ = 900

The sum of moments about point B is also zero (use clockwise as positive).

(T₁)(4.5)-300(2.25)-600(1.3) = 0

4,5T₁=1455

T₁ = 323,3N

T₂ = 900 - 323.3

T₂ = 576.7N

(The rope has a higher tension on the side closest to the window washer.)