If you have ever looked at the end of a crane, or if you have ever used an engine hoist or a come-along, or if you have ever looked at the rigging on a sailboat, then you have seen a block and tackle at work. A block and tackle is an arrangement of rope and pulleys that allows you to trade force for distance. In this edition of How Stuff Works we will look at how a block and tackle works, and also examine several other force-multiplying devices!
Understanding the Block and Tackle
Imagine that you have the arrangement of a 100 pound (45.4 kilogram) weight suspended from a rope, as shown here.
In this figure, if you are going to suspend the weight in the air then you have to apply an upward force of 100 pounds to the rope. If the rope is 100 feet (30.5 meters) long and you want to lift the weight up 100 feet, you have to pull in 100 feet of rope to do it. This is simple and obvious.
Now imagine that you add a pulley to the mix.
Does this change anything? Not really. The only thing that changes is the direction of the force you have to apply to lift the weight. You still have to apply 100 pounds of force to keep the weight suspended, and you still have to reel in 100 feet of rope in order to lift the weight 100 feet.
The following figure shows the arrangement after adding a second pulley:
This arrangement actually does change things in an important way. You can see that the weight is now suspended by two pulleys rather than one. That means the weight is split equally between the two pulleys, so each one holds only half the weight, or 50 pounds (22.7 kilograms). That means that if you want to hold the weight suspended in the air, you only have to apply 50 pounds of force (the ceiling exerts the other 50 pounds of force on the other end of the rope). If you want to lift the weight 100 feet higher, then you have to reel in twice as much rope 0- 200 feet of rope must be pulled in. This demonstrates a force-distance tradeoff. The force has been cut in half but the distance the rope must be pulled has doubled.
The following diagram adds a third and fourth pulley to the arrangement:
In this diagram, the pulley attached to the weight actually consists of two separate pulleys on the same shaft, as shown on the right. This arrangement cuts the force in half and doubles the distance again. To hold the weight in the air you must apply only 25 pounds of force, but to lift the weight 100 feet higher in the air you must now reel in 400 feet of rope.
A block and tackle can contain as many pulleys as you like, although at some point the amount of friction in the pulley shafts begins to become a significant source of resistance.
Other Force/Distance Tradeoffs
You come into contact with force/distance tradeoffs in all sorts of simple machines. For example, a lever is an example of this phenomenon:
In this diagram a force F is being applied to the left end of the lever. The left end of the lever is twice as long (2X) as the right end (X). Therefore on the right end of the lever a force of 2F is available, but it acts through half of the distance (Y) that the left end moves (2Y). Changing the relative lengths of the left and right end of the lever changes the multipliers.
Gears can do the same thing:
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In this diagram the left-hand gear has twice the diameter of the right-hand gear. For every turn of the left-hand gear, the right-hand gear turns twice. If you apply a certain amount of torque to the left-hand gear through one rotation, the right-hand gear will exert half as much torque but will turn two revolutions.
Another good example is a simple hydraulic system, as shown below:
Assume that you have two cylinders full of water with a pipe connecting the two cylinders together as shown. If you apply a force F to the left-hand plunger, it creates a pressure in the left-hand cylinder. Let's say you apply a 10 pound downward force to the left-hand cylinder. Let's also say that the radius of the left-hand cylinder is 0.57 inches. Therefore, the area of the left-hand piston is Pi * 0.57 * 0.57 = 1 square inch. If the radius of the right-hand cylinder is 4 times greater, or 2.28 inches, then the area of the right-hand piston is 16 square inches, or 16 times greater. If you push the left-hand piston down through 16 inches with a force of 10 pounds, then the right-hand piston will rise 1 inch with a force of 160 pounds. Hydraulic cylinders of all sorts take advantage of this simple force-multiplying effect every day.
You can see that a block and tackle, a lever, a gear train and a hydraulic system all do the same thing: they let you magnify a force by proportionally diminishing the distance through which the magnified force can act. It turns out that this sort of force multiplication is an extremely useful capability! Here are some of the devices that use these simple principles:
- Car jack (lever or threaded gear)
- Fingernail clippers (lever)
- Automobile transmission (gears)
- Come-along (block and tackle, gear)
- Can opener (gear, lever)
- Crowbar (lever)
- Hammer claw (lever)
- Bottle opener (lever)
- Car brakes (hydraulics)
- Hydraulic shop lift
- Elevator (block and tackle)