
Grandpa Pencil
learns about
The Velocity Ratio of
Simple Pulleys
A very useful form of machine for lifting is the pair of rope blocks (see right). A simple example of this consists of a pulley, groved to accommodate the rope, top and bottom with a rope threaded round as shown. Finding the velocity ratio (V.R.) of this 'simple machine' is best done by holding ropes (a) and (b) and lifting the bottom block bodily, say by 1 mtr. When the load (w) had been lifted both ropes (a) and (b) will each have 1 mtr of slack in them so (p) needs to be pulled 2 mtrs to take up the slack. Effort (p), therefore, moves 2 mtrs while the load (w) only 1. Therefore :




An easy rule here is that the V.R. is equal to the number of ropes to and from the moving block/s as well as the number of pulleys in the system (in the case above there are 2 and to the left there are 6.) In the illustration to the left we see a system of pulley blocks with three pulleys at the top block and three pulleys at the bottom block.An actual tripple pulley would not look like this as all the pulleys on each block would be on a common axle side by side.If W is lifted bodily by 1 mtr then each of the six ropes would have a slack of 1 mtr and P would have to be pulled 6 mtrs to take up the slack.In this example, then, V.R. equals 6 and there are six pulleys as well as six ropes to and from the moving pulleys proving, again, the formula:

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