### Archimedes` Law of Lever

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Tan Wang txw5149
What Is Lever
A lever is a machine consisting of a beam or
rigid rod pivoted at a fixed hinge or fulcrum.
It is one of the six simple machines
identified by Renaissance scientists.
A lever amplifies an input force to provide a
greater output force, which is said to
provide leverage. The ratio of the output
force to the input force is the ideal
mechanical advantages of the lever.
The law of Lever
Assuming the lever does not dissipate or store
energy, the power into the lever must equal the
power out of the lever. As the lever rotates around
the fulcrum, points farther from this pivot move
faster than points closer to the pivot.
Therefore a force applied to a point farther
from the pivot must be less than the force
located at a point closer in, because power is the
product of force and velocity.
If a and b are distances from the fulcrum to
points A and B and let the force FA applied to A is the
input and the force FB applied at B is the output, the
ratio of the velocities of points A and B is given by a/b,
so we have the ratio of the output force to the input
force, or mechanical advantage, is given by
MA = FB/FA = a/b
This is the law of the lever, which was proven
by Archimedes using geometric reasoning.
Clases
ClassesofofLever
Lever
Class 1: Fulcrum in the middle: the effort is applied on one side of
the fulcrum and the resistance on the other side, for example,
a crowbar or a pair of scissors.
Class 2: Resistance in the middle: the effort is applied on one side
of the resistance and the fulcrum is located on the other side, for
example, a wheelbarrow, a bottle opener or the brake pedal of a
car. Mechanical advantage is greater than 1.
Class 3: Effort in the middle: the resistance is on one side of the
effort and the fulcrum is located on the other side, for example,
a pair of tweezers or the human mandible. Mechanical
advantage is less than 1.
Archimedes
Clases
of Lever
The earliest remaining writings regarding levers date from
the 3rd century BC and were provided by Archimedes. "Give
me a place to stand, and I shall move the Earth with it“ is a
remark of Archimedes who formally stated the correct
mathematical principle of levers.
Archimedes was born c. 287 BC in the seaport city
of Syracuse, Sicily, at that time a selfgoverning colony in Magna Graecia, located along the coast
of Southern Italy. He died c. 212 BC during the Second Punic
War. The last words attributed to Archimedes are "Do not
disturb my circles", a reference to the circles in the
mathematical drawing that he was supposedly studying when
disturbed by the Roman soldier.
Lever
The Clases
law of of
Lever
Before
Archimedes
“Mechanica” is a work believed to have been written by
the Peripatetic School, which is the name given to the followers of
Aristotle. It was probably written in the years between the death
of Aristotle in 322 BC and the birth of Archimedes c. 287 BC.
The “kinetic” argument for the Law of the Lever given in the
passage comes close to the idea of energy as the product of force
and distance, to the concept of the conservation of energy, and to
the principle of virtual velocities. As such, it is a more seminal
argument than Archimedes’ “static” one, which does not provide
much insight as to why the law is valid. But Archimedes used
geometric reasoning to prove the law of lever.
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Clases
of
Lever
Effects of law of Lever
A lever is a simple machine that allows people to gain a
mechanical advantage in moving an object or in applying a
force to an object. It is considered a "pure" simple machine
because friction is not a factor to overcome, as in other simple
machines.
There are many things in our daily life use the law of law of
lever. Such as Scissors, a wheelbarrow, a bottle opener, a pair
of tweezers or the brake pedal of a car. The common uses of
the law of lever make people’s life more convenient.
References
Clases
of Lever
Davidovits, Paul (2008). "Chapter 1". Physics in Biology and
Medicine, Third edition. Academic Press. p. 10.
Uicker, John; Pennock, Gordon; Shigley, Joseph (2010). Theory
of Machines and Mechanisms (4th ed.). Oxford University
Press, USA.
Usher, A. P. (1929). A History of Mechanical Inventions.
Harvard University Press (reprinted by Dover Publications
1988).
A. P. Usher, 1929, A History of Mechanical Inventions, Harvard
University Press, (reprinted by Dover Publications 1968).
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