Simple Machines: Pulling with Pulleys
Ask Science explains how simple machines like pulleys can become force multipliers, helping you do twice as much work…but for a price.
Lee Falin, PhD
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Simple Machines: Pulling with Pulleys
“Force multiplication” is a term used by the military to refer to a technology or skill that makes a military force more effective. Guided missiles, physically fit troops, combat drones, body armor, and even good spirits are all examples of military force multipliers.
Well, it turns out that you use force multipliers every day, even if you’re not in the military. You see, a special set of force multipliers have been studied by scientists going all the way back to Archimedes. These force multipliers are called simple machines. A simple machine is a basic mechanical device that changes the magnitude or direction of a force.
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Quite the Advantage
Simple machines are considered force multipliers because they actually let you…multiply your force. Remember that force is equal to mass times acceleration, so a machine that lets you multiply your force will allow you to move heavier loads than you’d normally be able to, or to move them faster than you’d normally be able to. Just how much of a multiplication the machine gives to your force is called the mechanical advantage of the machine.
Wait a second; does this mean you’re getting something for nothing? Am I talking about some magic machine that can do your work for you? Unfortunately, no. Remember back when we were talking about work and we said that work is equal to force times distance? In other words, the amount of work you do is equal to the amount of force you apply to an object, multiplied by the distance the object moves.
A simple machine can’t change the amount of work you do, because work is equivalent to energy, and the law of conservation of energy doesn’t allow for energy to come from nowhere. Instead, a simple machine lets you trade distance for force.
Pulling with Pulleys
Imagine that one day you get a job renovating a dance club. One of the things the owners really want is to have a giant disco ball suspended from the ceiling. Unfortunately, the disco ball they’ve chosen weighs about 100 kg, and the ceiling is 10 meters high. Even though you’ve got a really, really tall ladder, you know that there’s no way you can lift something that heavy while you climb up.
Fortunately, right next to the spot in the ceiling where the disco ball needs to go is a set of pulleys (sometimes called a block and tackle). By using the pulleys, you’re able to multiply the amount of force you have to lift the giant disco ball. But nothing in life is free, and that includes lifting disco balls with pulleys.
Let’s say that the pulley system you’re using has a mechanical advantage of 2. This means for every newton of force you apply to the rope, two newtons of force will be applied to the disco ball. However, since work is equal to force times distance and since the amount of work that you perform can’t be changed by the pulley:
Work Input = Your Force x Your Distance = Disco Ball Force x Disco Ball Distance = Work Output
Work Input = 1 Newton x Your Distance = 2 Newtons x Disco Ball Distance = Work Output
In other words, with a mechanical advantage of 2, you get twice us much force, but you have to pull the rope twice the distance that the disco ball moves. So for every meter of height that the disco ball goes up, you need to pull 2 meters of rope.
Some block and tackle setups can give you even higher mechanical advantage, but every multiple of force you get increases the amount of distance you have to move in order to do the same work. A mechanical advantage of 4 lets you lift 4 times as much as you normally could (which means the disco ball will feel like it only weighs 25 kg), but requires that you pull 40 meters of rope in order to lift the ball 10 meters high.
Conclusion
So now you understand what mechanical advantage is, and how simple machines can be used to multiple your force. You also know that since work = force x distance, and since simple machines don’t change the amount of work you do, your increased force comes at the price of an increased distance. Pulleys are just one type of simple machine. In our next episode we’ll take a look at another simple machine, the lever.
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Pully image courtesy of Shutterstock
