The lever is a simple machine consisting of a movable rod fixed at a point, or fulcrum. Among the six simple machines, the lever is one of the two "Parent Machines" that the others are based off of, along with the inclined plane. There are three classes of levers: first class, second class, and third class. Like many machines, levers can reduce the force required to accomplish a task by increasing the distance that the force must be applied to. (Mechanical Advantage greater than one) However, levers can also increase the distance and speed that something moves while increasing the force needed to be applied. (Mechanical Advantage less than one) The space between the fulcrum and the load (what the lever is moving, or the force is being applied to) is called the load arm. The space between the fulcrum and the effort (where force is being applied) is called the effort arm. Levers generally have a higher mechanical efficiency than inclined planes, because there are less rubbing surfaces to create friction.
First class levers have the fulcrum located between the load and effort. The load arm is generally shorter than the effort arm, but it can be the reverse. By increasing the distance that the effort is exerted, less force is needed. However, if the effort arm is shorter than the load arm, then more force will need to be applied to less distance in order to move a load farther and faster. Since the load arm can be longer, the effort arm can be longer, on both arms can be equal, the mechanical advantage of this type of lever can be less than, greater than, or equal to one. In a first class lever, the effort is applied in the opposite direction to the direction that the load moves.
In a second class lever, the load is located between the effort and fulcrum. As a result of this, the effort arm is always longer than the load arm. By increasing the distance that the effort is exerted, less force is needed. That means that the mechanical advantage of this type of lever is always greater than one. In this type of lever, the direction of the effort is the same as the direction in which the load moves.
In a third class lever, the effort is exerted between the load and the fulcrum. As a result of this, the load arm is always longer than the effort arm. As well, the effort and load move in the same direction. Since the load arm is longer, more force is required to move it, but it moves at a faster speed. This also means that the mechanical advantage of this type of lever is always less than one. This is very common in sports in which a stick is used to propel something at a high speed.
"ΤΑ ΜΕΓΕΘΕΑ ΙΣΟΡΡΟΠΕΟΝΤΙ ΑΠΟ ΜΑΚΕΩΝ ΑΝΤΙΠΕΠΟΝΘΟΤΩΣ ΤΟΝ ΑΥΤΟΝ ΛΟΓΟΝ ΕΧΟΝΤΩΝ ΤΟΙΣ ΒΑΡΕΣΙΝ." ("Magnitudes are in equilibrium at distances reciprocally proportional to their weights.")
-Archimedes
What it means
That may seem confusing, ("...equilibrium at distances reciprocally proportional..."?) but it is really quite simple. The law of the lever basically states that on a first class lever, the distance that a load and effort ("Magnitudes") must be from the fulcrum in order to balance (to be "in equilibrium") depends on their weights. (Archimedes illustrated the point with weights, but the same principle applies to non-gravitational forces.) If two 100 kg weights are placed on a lever, they each exert an approximate force of 980 N. (Gravity attracts the weights with force of 9.8 N/kg. 100 * 9.8 = 980) Since the forces are equal, their distances from the fulcrum must be the same. If one of the weights were just a 980 N force (effort) and the other weight (load) were to be 700 kg instead, the weight would exert a force of approximately 6860 N. Since 6860 N is 7 times greater than 980 N (or that 700 kg is 7 times greater than 100 kg) the load arm arm would have to be 7 times shorter than the effort arm ("reciprocally proportional") to remain balanced. If the load arm were even shorter than one-seventh of the effort arm, the load would rise. If the load arm were longer than one-seventh of the effort arm, it would remain on the ground, and no work would be done, despite the 980 N of force being exerted as the effort.
Could Archimedes have lifted the Earth?
We have probably all heard that Archimedes once claimed that if he had a place on which to stand on a fulcrum, he could have used a lever to lift the Earth. (For argument's sake, let's assume that "lifting the Earth" would mean lifting an object with the mass of Earth being affected by Earth's gravity.) Unfortunately, even assuming that he had what he desired, (a place to stand and a fulcrum) this would still prove impossible. Astronomers know Earth's mass. On Earth, an object of this mass would weigh approximately 6,000,000,000,000,000,000,000 tons. Assuming Archimedes could lift 60 kg without assistance, the effort arm would need to be longer than the load arm by 100,000,000,000,000,000,000,000 times! If the end of the load arm were to move even 1 centimeter, the end of the effort arm would need to travel 1,000,000,000,000,000,000 km. This already seems impossible. However, assuming that he could lift 60 km at 1 meter per second, (almost 1 horsepower) then that would take 1,000,000,000,000,000,000,000 seconds, or 30,000,000,000,000 years! Even if Archimedes could have moved his end of the lever at 300,000 km/second, (the speed of light) lifting the Earth 1 cm would take 10,000,000 years.
Interactive lever
The interactive lever below is a first class lever.
Requires Wolfram CDF Player plugin by Wolfram Research (It's free)
Sometimes, it is necessary to move a load in a full 360o circle. (For example, when you reel a fishing line, you must move the end of the line around in a circle several times to wind it into a coil.) In this case, the fulcrum (now called an axle) becomes a rod that lever rotates around. This type of lever is known as a wheel and axle, which is more commonly shortened to a wheel. Though conventional wheels are circular, this needn't be the case.
Note
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Three Classes of Levers
First Class Levers
First class levers have the fulcrum located between the load and effort. The load arm is generally shorter than the effort arm, but it can be the reverse. By increasing the distance that the effort is exerted, less force is needed. However, if the effort arm is shorter than the load arm, then more force will need to be applied to less distance in order to move a load farther and faster. Since the load arm can be longer, the effort arm can be longer, on both arms can be equal, the mechanical advantage of this type of lever can be less than, greater than, or equal to one. In a first class lever, the effort is applied in the opposite direction to the direction that the load moves.
Examples
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Second Class Levers
In a second class lever, the load is located between the effort and fulcrum. As a result of this, the effort arm is always longer than the load arm. By increasing the distance that the effort is exerted, less force is needed. That means that the mechanical advantage of this type of lever is always greater than one. In this type of lever, the direction of the effort is the same as the direction in which the load moves.Examples
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Third Class Levers
In a third class lever, the effort isExamples
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Law of the Lever
"ΤΑ ΜΕΓΕΘΕΑ ΙΣΟΡΡΟΠΕΟΝΤΙ ΑΠΟ ΜΑΚΕΩΝ ΑΝΤΙΠΕΠΟΝΘΟΤΩΣ ΤΟΝ ΑΥΤΟΝ ΛΟΓΟΝ ΕΧΟΝΤΩΝ ΤΟΙΣ ΒΑΡΕΣΙΝ." ("Magnitudes are in equilibrium at distances reciprocally proportional to their weights.")-Archimedes
What it means
That may seem confusing, ("...equilibrium at distances reciprocally proportional..."?) but it is really quite simple. The law of the lever basically states that on a first class lever, the distance that a load and effort ("Magnitudes") must be from the fulcrum in order to balance (to be "in equilibrium") depends on their weights. (Archimedes illustrated the point with weights, but the same principle applies to non-gravitational forces.) If two 100 kg weights are placed on a lever, they each exert an approximate force of 980 N. (Gravity attracts the weights with force of 9.8 N/kg. 100 * 9.8 = 980) Since the forces are equal, their distances from the fulcrum must be the same. If one of the weights were just a 980 N force (effort) and the other weight (load) were to be 700 kg instead, the weight would exert a force of approximately 6860 N. Since 6860 N is 7 times greater than 980 N (or that 700 kg is 7 times greater than 100 kg) the load arm arm would have to be 7 times shorter than the effort arm ("reciprocally proportional") to remain balanced. If the load arm were even shorter than one-seventh of the effort arm, the load would rise. If the load arm were longer than one-seventh of the effort arm, it would remain on the ground, and no work would be done, despite the 980 N of force being exerted as the effort.Could Archimedes have lifted the Earth?
We have probably all heard that Archimedes once claimed that if he had a place on which to stand on a fulcrum, he could have used a lever to lift the Earth. (For argument's sake, let's assume that "lifting the Earth" would mean lifting an object with the mass of Earth being affected by Earth's gravity.) Unfortunately, even assuming that he had what he desired, (a place to stand and a fulcrum) this would still prove impossible. Astronomers know Earth's mass. On Earth, an object of this mass would weigh approximately 6,000,000,000,000,000,000,000 tons. Assuming Archimedes could lift 60 kg without assistance, the effort arm would need to be longer than the load arm by 100,000,000,000,000,000,000,000 times! If the end of the load arm were to move even 1 centimeter, the end of the effort arm would need to travel 1,000,000,000,000,000,000 km. This already seems impossible. However, assuming that he could lift 60 km at 1 meter per second, (almost 1 horsepower) then that would take 1,000,000,000,000,000,000,000 seconds, or 30,000,000,000,000 years! Even if Archimedes could have moved his end of the lever at 300,000 km/second, (the speed of light) lifting the Earth 1 cm would take 10,000,000 years.Interactive lever
The interactive lever below is a first class lever.Requires Wolfram CDF Player plugin by Wolfram Research (It's free)
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Other Types of Levers
Sometimes, it is necessary to move a load in a full 360o circle. (For example, when you reel a fishing line, you must move the end of the line around in a circle several times to wind it into a coil.) In this case, the fulcrum (now called an axle) becomes a rod that lever rotates around. This type of lever is known as a wheel and axle, which is more commonly shortened to a wheel. Though conventional wheels are circular, this needn't be the case.Examples
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Bibliography
Image Source
www.aaronswansonpt.com/Information Sources
Perelman, Yakov. Physics for Entertainment. New York: Mir Publishers, 1975.Rorres, Chris. "Law of the Lever." Courant Institute of Mathematical Sciences. New Youk University. 2 Apr. 2013 <http://www.math.nyu.edu/~crorres/Archimedes/Lever/LeverLaw.html>
Sandner, L et al. Investigating Science and Technology 8. Canada: Reid McAlpine, 2008.
Other
Blinder, S. M. "Principle of the Lever." Wolfram Demonstrations Project. Wolfram Research. 5 Apr. 2013 <http://demonstrations.wolfram.com/PrincipleOfTheLever/>Return to Top
Note
I apologize for the advertisements placed over the words such as "classes." WikiSpaces just does that. It's out of my control. Even AdBlock for Google Chrome doesn't fix the issue. I hate advertisements just as much as I'm sure that you do, (especially when they're disguised as hyperlinks) but please also understand that owning a web domain name requires money.
--Neel
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