Simple Machines: Working Together (1984)

[Music] Suppose you were an inventor and you built machines to help you do work. Probably some of the machines would have only a few moving parts and some would have many moving parts. But the more machines you made, the more you'd find yourself using certain mechanical parts over and over again. The inclined plane, the pulley, the wheel and axle, and the lever. These are the simple machines, the basic building blocks of mechanical devices. Each simple machine can be used just by itself. But in machines with several moving parts, there are often two or more simple machines linked together to do one job. To see exactly what happens when simple machines work together, we need to look at some basic things they all do separately. For instance, all simple machines make work easier. Here is a lever being used to do work. This is work. Well, to a scientist, work means something special. Scientists use an equation that says work equals force * distance or W= F * D. This means that when your foot exerts a force to move something through a distance, you do work. In this case, this is the input work. The force you exert times the distance that force moves your end of the lever. But when you do this, you cause the other end of the lever to move also. And when it does, it also exerts a force that moves something through a distance. So it too does work. This is the output work. With all simple machines, the input work and the output work are equal except for small losses through friction. Now the input work is equal to its force times distance and the output work is equal to its force times distance. So for all simple machines the input force times its distance and the output force times its distance have to be equal. But if they're equal, how can a simple machine make your work easier? While the two sides of the equation have to be equal, nothing says that the two forces have to be equal or that the two distances have to be equal. Only their products have to be the same. And it's because of this fact that simple machines can help us do work. Here's a lever with its fulcrum not in the middle. Suppose you want to raise this stump out of the ground. To do that, the lever has to exert, say, 60 lb of force here. If you need to raise the stump 2 feet, that would be 60 lb* 2t or 120 ft-lb of output work that the lever has to do. So, your input also has to equal 120T-lb of work. But notice that now your end of the lever moves a greater distance than the other end. While the output end moves a distance of 2 feet, your end moves 6 ft. 6 * what equals 120? 20. So you need to apply only 20 lb of force. F * D still equals F * D. And now with 20 lb of force, you can lift a 60 lb load. You and the lever do the same amount of work, but you trade increased distance on your end to get increased force on the other end. You can make a similar trade with any other simple machine. For instance, with a pulley system. When this end of the rope moves a certain distance, this pulley system will move a load placed here only 1/4 as far. But when a force is applied here, the pulley system exerts four times as much force here to lift a [Music] load. Again, you trade increased distance to get increased force. But sometimes you don't want to get more force, you want to get more distance instead. Most simple machines can also help you do this. For instance, using a fishing pole as a lever, you can get this end to move a large distance to raise your catch while you push this end down only a small distance. With the fulcrum here, when you push your end down one foot, the other end moves four feet. If your catch weighs three lbs, the output work equals 3 lb* 4t or 12t-lb of work. Since there has to be the same amount of work here at the input end, which moves only 1 ft, you have to push down with 12 lb of force. F * D still equals F * D. So with this lever, you do the opposite of what you did before. Now you trade a large force to move something a large distance. So with simple machines you can put in increased distance to get an output of increased force or you can put in increased force to get an output of increased distance because you always trade one for the other. A simple machine can't increase both force and distance at the same time. But depending on how you build simple machines, you can control the amount of the trade. An easy way to think about this is to use the idea of mechanical advantage. That's the amount the simple machine multiplies the input force. Mechanical advantage is especially useful in understanding what happens when simple machines work together as they do in this bolt cutter. To see how it works, you can think about just one side since it's a mirror image of the other side. You apply your force here to this lever which happens to be bent. It works the same way a straight lever does. This is the fulcrum. This lever applies its force to this lever. Here's its fulcrum. And you use the output force of this lever to cut something here. But exactly how do all these forces work? In levers, mechanical advantage is determined by how much longer one arm is than the other. In this lever, the long arm is 15 times as long as the short arm. So the mechanical advantage of this lever is 15. And on this lever, this arm is three times as long as this arm. So the mechanical advantage here is three. But and here's the key to how simple machines work together. Notice that the output force of this lever is the input force of this lever. When simple machines work together this way, the whole arrangement is called a compound machine. To find the mechanical advantage of a compound machine, you multiply the mechanical advantages of the separate machines in it. Suppose you apply 20 lb of force here. Then the other end of this lever applies 20 lb times the mechanical advantage 15 or 300 lb of force. But that force 300 lb becomes the input force of this lever. And this lever further multiplies it by its mechanical advantage three making these levers cut with 3 * 300 or 900 lb of force here. The output is this great because your input is multiplied by the two mechanical advantages together. 15* 3 or 45. So 45 is the mechanical advantage of the whole compound machine. The arms of a bolt cutter combine simple machines of the same type, all levers. But often you combine different kinds of simple machines. You do this, for instance, when you use a simple automobile jack. This crank works as a wheel and axle machine. You can think of the path the handle follows as a large wheel which turns this axle. The axle turns another much smaller wheel here. And that simple machine supplies the input force for the other simple machine. These screw threads. Screw threads are really just an inclined plane that's wrapped around a core. The input force here causes the screw threads to turn, pulling these two points toward each other. The rest of the mechanism just makes this sideways force push up. The mechanical advantage of the crank is about 20. And the mechanical advantage of the screw threads is about 15. That makes a compound mechanical advantage of 20 * 15 or 300. So, if you apply 30 lb of force here, this jack will lift 30 lb* 300 or 9,000 lb. So, it's possible to get tremendous mechanical advantages by combining two simple machines. But many compound machines combine more than two simple machines. If you take a wheel and axle machine and use it to wind up a rope that goes to a pulley system, you have the basic parts of a crane. But in most cranes, the input force from the engine is multiplied before it gets to this point by at least one other wheel and axle machine. The compound mechanical advantage equals the mechanical advantages of all three simple machines multiplied together. So a crane can produce an extremely great lifting [Music] force. So with simple machines, you can make your work easier by trading distance for force or force for distance. And when simple machines work together in a compound machine, your trade can be very large because the mechanical advantage can be extremely great. [Applause] [Music] Done.