A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 190 N and is 3.4 m long. What is the tension in each rope when the 702–N worker stands 1.08 m from one end?

Tension at rope A is 317.99 N, and Tension at rope B is 574.01 N

Explanation:

The weight of the scaffolding is 190 N

The length of the scaffolding is 3.4 m

The worker stands 1.08 m from one end, that is (3.4 - 1.08)m from the other end

The weight of the worker is 702 N

This is a problem that can be resolved by considering the moments generated along the length of the scaffolding.

We have to note that the weight of the scaffolding will act at the middle, i.e at  a point 1.7 m from any end of the scaffolding.

We  proceed by taking the moment about each end. We designate the ends as A and B, where A is the end at the left side, and B is the end at the right side, and Ta and Tb as the tensions on the ropes at these ends.

We further state that the worker is standing at 1.08 m from the end B, i.e 2.32 m from point A

Moment = force x (perpendicular distance)

Also, since the scaffolding is stable, the total moments on the scaffolding balances out.

Let us consider the moment about point A: we take the point A as the hinge

moment due to weight of the scaffolding = 190 x 1.7 = 323 N-m (clockwise)

moment due to the weight of the worker = 702 x 2.32 = 1628.64 N-m (clockwise)

moment due to the tension on the rope at point B = Tb x 3.4 = 3.4Tb (anticlockwise)

Balancing the clockwise moments against the anticlockwise moments, we have..

323 + 1628.64 = 3.4Tb

1951.64 = 3.4Tb

Tb = 1951.64/3.4 = 574.01 N

Something to also note, is that, since the scaffolding is not moving up or down, then the upward forces is balanced by the downwards forces.

Total downward forces = 190 + 702 = 892 N

total upwards force = Ta + Tb

equating, we have

Ta + Tb = 892

but Tb = 574.01 N, therefore

Ta + 574.01 = 892

Ta = 892 - 574.01 = 317.99 N

This implies that Tension at rope A is 317.99 N, and Tension at rope B is 574.01 N

c. magnitude and direction