The number of rope strands supporting the load in a multiple-pulley system essentially correlates to the system's mechanical advantage. For example, if you have two fixed and two moveable pulleys, four lengths of rope with a mechanical advantage of four sustain the weight. As you add more pulleys, the rope lengths need to be adjusted to maintain the same overall mechanical advantage.
In conclusion, the total effective rope length in a multiple-pulley system is equal to the sum of the individual rope lengths used to lift the load divided by the mechanical advantage of the system.
By increasing the quantity of rope used to hoist the object, using numerous pulleys reduces the amount of force required to move it. A pulley system's mechanical advantage (MA) is equal to the number of ropes supporting the moveable weight. For example, if four separate ropes are used to lift a load that would require only one rope to lift it if no pulleys were used.
In simple terms, a MA gives an instrument or machine a power of lifting much more than its own weight. For example, a MA of 10 allows something that is weightless (i.e., not carrying any weight) to be lifted 10 times its size with just as much effort as it takes to lift something that weighs 1 kilo (2.2 pounds). Maces, sledgehammers, and other heavy tools used by ancient warriors were often attached to a belt for easy access. This invention allowed them to be used effectively without being carried by their owners.
There are two types of MAs: direct and indirect. With a direct MA, one end of the device pulling on the rope provides all the force necessary to lift the load. An example of this type of MA is when one person pulls on one end of a cable to raise a crane. The crane operator doesn't have to provide any additional force to keep the load raised because the person pulling on the cable is doing so completely under his or her own power.
A pulley system's optimal mechanical advantage is equal to the number of rope segments bearing the weight. Doing the lifting is more beneficial for the rope parts. If the load is too heavy for a single segment, then multiple ones should be used.
Optimal mechanical advantage can be higher or lower than one. For example, a bow drill has a mechanical advantage of 10:1 because it uses only one piece of wood for its shaft. If you made a bow drill with a hundred-pound weight on top, it would break under its own weight before the shaft would reach maximum bending strength! A lever has infinite mechanical advantage because the force applied to the handle equals the load placed on the fulcrum (the other end of the lever). In general, a mechanism with many small levers having moderate loads attached to their centers will have high mechanical advantage.
The mechanical advantage of a machine such as a pulley system depends on how the load is distributed among the components. If the load is not evenly divided up, then more components will be required to do the same work as fewer components would if the load were equally divided.
Distance is the variable that varies. When employing a pulley system, you use less force to lift a load but must pull more rope to raise the load to a specific height. With a double pulley system, you must draw twice as much rope; with a triple pulley system, you must pull three times as much rope, and so on. The lifting power of these systems is therefore directly proportional to the number of ropes used.
For example, if you have a 100-pound load and need to lift it up 10 feet, you would need 10 pounds of force. If you used a single pulley system, it would take 10 pounds of force to lift the load 10 feet. But if you used a double pulley system, it would take 20 pounds of force, because 10 pounds comes from each side of the pulleys. A triple pulley system would require 33 pounds of force, and so on.
The total lifting force required is the product of the distance lifted and the load weight. So, in this case, we can say that the force required is 10 x 100 = 1000 pounds. This means that it takes 1,000 pounds to lift the load 10 feet with two pulleys, 2,000 pounds to lift it 15 feet, and so on.
As you can see, the lifting force increases proportionally to the number of pulleys used. However, the amount of work done by each person working the rope is the same for all numbers of pulleys used.
To calculate a pulley's mechanical advantage, just count the number of rope sections that support whatever object you are raising (not counting the rope that is attached to the effort). In a one-pulley system, for example, the MA is 1. The MA in a two-pulley system is 2. In a three-pulley system, it is 3, and so on.
For example, if we were to use a one-pulley system to lift an object that weighs 50 pounds, the MA would be 1/50 = 0.02. If we used a two-pulley system, the MA would be 1/(50/2) or 1/10. If we used a three-pulley system, the MA would be 1/(50/3) or 1/15.
As you can see, the mechanical advantage of using more than one pulley to lift an object is equal to the lowest number of ropes needed to lift the object. So, for example, if five pieces of string were needed to lift an object that normally would require only two pieces of string, then the MA is 5/2 = 2.5.
It should be noted that the mechanical advantage does not take into account the weight of the person operating the pulleys.
How can the mechanical advantage of a pulley system be calculated? Count the number of rope or cable segments, including the free end, on each side of the pulleys. Subtract 1 from this amount if the free end is to be dragged down. The resulting number is the calculation for the mechanical advantage.
In this example, there are two segments of rope or cable on one side of the pulley and three segments on the other. Therefore, the mechanical advantage is 3:1. This means that for every three feet that you pull down, one foot will be pulled up. You can test this out by pulling down on the free end of the rope or cable for several minutes. It should become taut; otherwise, the mechanism has failed.
A pulley system's mechanical advantage determines how much force is required to operate it. A high mechanical advantage means you need a lot of force to start it moving; a low one means you can start it with just your hand. A lever whose mechanical advantage is less than 1:1 requires only your hand for operation. One where the mechanical advantage is more than 1:1 needs only a small force to start it moving.
Pulleys are used in many mechanisms including cranks, camshafts, and wheels. They can also be used as brakes by applying pressure to the belt or rope that goes through them.