# The painter's lift

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 (tying 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 $$F_1$$ be the force the worker exerts on the hanging rope in the painter's lift configuration to move upward at a constant speed. Let $$F_2$$ be the force the worker would need to exert on a single rope to move upward at a constant speed. What is $$F_1/F_2$$? You can assume the rope itself doesn't have any significant mass.

Details and assumptions

• You may assume the rope is effectively massless.
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