In the photo above, the lever is set-up to connect the input at 3" and the output at 6" from the fixed pivot. In this position, the output will move two times as far as the input. Why is this?
The distance moved by the output is determined by the ratio of the input arm to the output arm. When the ratio of input to output arm is 1:2, the output moves twice as far as the input. If the input link or output link is connected to the lever at a distance that results in a ratio different than 1:2, then the output will not move twice as far as the input.
For example, suppose that in Experiment C, the output was moved to the 10" hole, but the input left at the 3" position rather than being moved to the 5" position. When the input and output are connected at 5" and 10" respectively, their ratio is 1:2 and the output moves twice as far as the input. However, if the input is at 3" and the output at 10", then the ratio of input arm to output arm is 3:10. The output will move 10/3 (or3 1/3) times as far as the input.