Workers who wash windows or paint the outside of buildings use an interesting contraption known as a painter's lift. This consists of a harness that the worker wears suspended by a rope. The rope runs through a pulley mounted on the roof of the building and back down to hang beside the worker. The worker simply pulls down on the hanging rope to raise herself up, and releases it to lower herself down (tieing the hanging rope to her harness keeps her at a constant height). What's neat is that the configuration also makes it easier for the worker to move up and down than if she was just hanging by a single rope. Let F1 be the force the worker exerts on the hanging rope in the painter's lift configuration to move upward at a constant speed. Let F2 be the force the worker would need to exert on a single rope to move upward at a constant speed. What is F1/F2? You can assume the rope itself doesn't have any significant mass.

Question

Workers who wash windows or paint the outside of buildings use an interesting contraption known as a painter's lift. This consists of a harness that the worker wears suspended by a rope. The rope runs through a pulley mounted on the roof of the building and back down to hang beside the worker. The worker simply pulls down on the hanging rope to raise herself up, and releases it to lower herself down (tieing the hanging rope to her harness keeps her at a constant height). What's neat is that the configuration also makes it easier for the worker to move up and down than if she was just hanging by a single rope. Let F1 be the force the worker exerts on the hanging rope in the painter's lift configuration to move upward at a constant speed. Let F2 be the force the worker would need to exert on a single rope to move upward at a constant speed. What is F1/F2? You can assume the rope itself doesn't have any significant mass.

Answer 1

The tension in the rope T pulls up on the worker's hand while the tension in the rope T also pulls up on the harness. Therefore the total force up on the worker is 2T. The force down is W, the weight. The acceleration is zero.

therefore T = W/2 and F1/F2 = 1/2
In other words the mechanical advantage is 2

Answer 2

This is the exact wording of one of this week's problems on brilliant dot o r g

Answer 3

To determine the ratio of F1 to F2, let's analyze the forces acting on the worker in each case.

In the painter's lift configuration:
1. Gravity exerts a downward force on the worker, equal to her weight, which we'll denote as W.
2. The worker exerts an upward force, which we'll denote as F1, by pulling down on the hanging rope.

In the single rope configuration:
1. Gravity exerts a downward force on the worker, equal to her weight, which is still W.
2. The worker exerts an upward force, which we'll denote as F2, by pulling up on the single rope directly.

Now, ideally, the worker wants both F1 and F2 to balance out the gravitational force so that she can move at a constant speed. This means that F1 = W and F2 = W.

To find the ratio of F1 to F2, we can substitute F1 = W and F2 = W into the equation:

F1/F2 = W/W = 1

So, F1/F2 is equal to 1. This means that the force exerted by the worker in the painter's lift configuration (F1) is the same as the force she would need to exert in the single rope configuration (F2) to move upward at a constant speed.