What Is an Example of a Block & Tackle Pulley System?
A block-and-tackle hoist or pulley system uses pulleys in groups called blocks. "Tackle" refers to the line that travels through the pulleys. The combination of several pulleys into one block may seem redundant at first, but it provides significant leverage, or mechanical advantage, much as a lever and fulcrum reduces the force needed to move a load. Block-and-tackle systems are common in nautical use, which was, historically, probably its first use.
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Leverage
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Having so many pulleys together in a block actually provides extra leverage. Suppose the puller of the line pulls out 10 feet of rope, but the load rises only two feet. The mechanical advantage was 5-to-1, and the puller had to pull with a force of only a fifth the weight of the load, albeit over a greater distance.
This is analogous to a fulcrum placed so that the load end of the lever is only one unit long, while the pushing end is five units long, again gaining a mechanical advantage of 5-to-1.
The advantage comes from the law of conservation of energy, since force times the distance applied equals work (energy) performed. Low force times great distance of application is the same as high force (load) times short distance.
An Inefficient Pulley Example
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Vertical lines are most desirable, so that no lateral force is introduced to increase the tension. For example, in the diagram, the slanted lines not only have to hold the load but also fight the lateral force each produces against the other. For the two diagonal lengths in the diagram, their tension is being used only obliquely to fight the vertical direction of gravity on the load. This is an important benefit of keeping pulleys in one block.
To put numbers to it, imagine the load in the diagram weighs 100 Newtons. If the lines were all vertical, the mechanical advantage of the pulley system would be 4-to-1, because four lines would each need to shorten a unit for the load to lift one unit. In other words, the puller would have to pull the rope four units. Then each line would be pulling up 25 Newtons. But with the introduction of lateral force, the tension is more than 25 Newtons on each line, and the puller has to tug with more than 25 Newtons just to hold the load off the ground.
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An Example from Archimedes
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Archimedes is believed to have invented the block-and-tackle system. He boasted of knowing how to pull a boat through water using only his own power. When King Kieron heard of this, he challenged Archimedes to make good on the boast. Archimedes then rigged up a block-and-pulley system, and pulled an entire warship, full of men and cargo, through the water with his own power.
Differential Pulley
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Another example of a block and tackle is a differential pulley, which is often seen in auto repair garages with one part of the closed loop left dangling. A differential pulley differs from a regular block and tackle in that one wheel of the block is a little smaller than the other; also, the pulleys in the block are fixed to each other. The tackle is a closed-loop chain, passing through all three pulleys. If the pulleys in the block were the same size, the load could not be lifted at all: A rotation of the block pulleys would let out the same length the other pulley would take up. But since one pulley is smaller, the load can be lifted. Since so much chain length must be pulled for a small load lift, the mechanical advantage is tremendous. Despite the ability to lift it, the load's pulling on both sides of the block keeps the block pulleys from unwinding, since the larger and smaller pulleys are connected. The pulling part of the chain can therefore hang loosely while the load is off the ground.
Mechanical Advantage
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To calculate the mechanical advantage of a differential pulley, ask what distance gets taken up in one turn of the block pulleys. Suppose the larger pulley in the block has radius R and the smaller has radius r. Then in one turn of the pulley block, the smaller pulley will release 2πr length of chain. The larger pulley, which is connected to the smaller pulley, will have taken up 2πR length of chain. So there is 2π(R-r) less chain on which the load is swinging. Because of doubling up, the load has been lifted half this distance, or π(R-r). Meanwhile, the length of chain the lifter pulled to cause the pulley block to turn one rotation is 2πR. So the mechanical advantage is distance pulled divided by distance lifted = 2πR / [π(R-r)] = 2R/(R-r). The closer r is to R, the larger the mechanical advantage.
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References
- Photo Credit Flickr/reivax
