# Pulleys

A three pulley system is set up with a harness so children can pull themselves upward. A rope is tied to the harness and runs up to the ceiling and through a pulley attached to the ceiling, down to the child and through a pulley on the harness, back up to the ceiling and through another pulley attached to ceiling, then back down to the child, who pulls on the rope themselves.

If the child does not want to pull themselves up, an alternative arrangement has the rope running through a redirect on the child's harness and being pulled by an adult.

If the child pulls the fourth rope the pulley system is 4:1, and the child finds it quite easy to pull themselves upward.

If the child pulls the second rope (so the second and third pulleys are unused and slack is taken in by an adult) the pulley system is 2:1. The child finds it very hard to pull themselves upward, but possible with determination.

If the child is pulled up by an adult the system is 3:1. The third pulley, at the top, acts only as a redirect.

These system ratios are from the length of rope needed to be pulled compared to the height the child is raised through. When the child pulls on the rope themselves, the force they apply on the rope counteracts their weight force by the amount they pull, which meant their weight is distributed across four rope sections (or two).

When an adult pulls the child up, the child's weight is distributed across three rope sections.

The three pulleys used were a Petzl Tandem Speed (two pulleys) and a Petzl Pro Traxion (version 1). Each of the pulleys has a rated efficiency of 95%. (This is very good for pulleys of this size.)

 Efficiency of a pulley system = useful energy ––––––––––– input energy = load * load distance ––––––––––––––––– force * force distance

Using a carabiner instead of a pulley generally has very low efficiency, but has a large variation, from 53% to 74%.

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