Transcript Lever

By： Yi Zheng
Jinxin Chen
Chengwei Ge
Yaqi Yang
Qian Xiao
In the lecture 07B we learned Torque.
Once we saw Torque, lever appeared in our
mind, because there is a principle called: The
2rd Principle of Leverage. This really
interests us. Hence, this time we are going to
tell something about Lever, Leverage and
these principles.
Before the introduction of how lever and torque
related to each other, let’s find out what is
lever first…
What is lever
• In physics
A lever is a rigid object that is used with an
appropriate fulcrum or pivot point to multiply
the mechanical force /effort that can be applied
to another object/load.
Information from Wikipedia
http://en.wikipedia.org/wiki/Lever
Category of the lever
Then, we learned from website that lever
has three classes. These classes represent
variation in the relative locations of the
fulcrum, the load and the force.
Information from Wikipedia
http://en.wikipedia.org/wiki/Lever
The first Class:
The fulcrum is located between the
applied force and the load. In this class,
seesaw, crowbar and scissors are all great
examples.
Information from Wikipedia
http://en.wikipedia.org/wiki/Lever
The second Class:
The load is situated between the fulcrum
and the force. Wheelbarrow and nutcracker
can clearly explain this class’s characteristic.
Information from Wikipedia
http://en.wikipedia.org/wiki/Lever
The third Class:
The force is applied between the fulcrum
and the load. Tweezers and mandible are
under this class.
Information from Wikipedia
http://en.wikipedia.org/wiki/Lever
However those three classes seemed not that
pragmatic in our daily life. So, after further
study, we found another classification of lever,
this method is obviously easier to understand…
According to the different effects lever has,
the lever can also be divided into another
three types.
Respectively, they are: saving-power lever;
laborious-power lever; equal-power lever
Saving-power lever
• Definition: the lever which has the power
greater than the resistance arm of the lever
arm
• Advantage: save force and power
• Disadvantage: need relative long distance
Equal-power lever
• Definition: the lever which has the force
equal to the resistance arm of the lever arm
• Advantage: -----• Disadvantage:------
Notice: Since this kind of lever is neither save the power nor
save the distance, we are not sure what are its strong points
and drawbacks.
Laborious-power lever
• Definition: the lever which has power less
than the resistance arm of the lever arm
• Advantage: short distance
• Disadvantage: laborious
Then, It comes to the LEVERAGE…
Leverage
Leverage is also been
called as “the equilibrium
conditions of lever”. To
make lever attain
equilibrium state, the
number of forces acted
upon on the two points of
the lever must have
inverse relationship with
their force arms
Mathematical Expression
• Mechanical force × Power arm =
Resistant force × Resistance arm
• Using algebra to express it as
F1 • L1 = F2 • L2
• In this expression,
F1 stands for mechanical force
L1 stands for power arm,
F2 represents resistant force
L2 represents resistance arm
After understanding what is lever and
leverage. It is high time to turn the page
and learn those marvelous principles
created by physicists.
Introductory to the principle &
History background
Archimedes, ancient Greek scientist,
once said
“give me a fulcrum and I will be able to
lever up the whole earth”
The portrait of Archimedes
Archimedes’ Achievement :
Archimedes in On the plane
figure of the balance was first
presented in his book leverage.
He began to leverage some
experience in the practical
application of knowledge as a
"self-evident axiom", and then
proceed from these axioms,
the use of geometry through the
strict logical demonstration,
come to the lever principle
These axioms are:
(1) without the weight of the rod ends of equal
distance from the pivot mount equal weight,
they will balance
(2) without the weight of the rod ends at equal
distances from the pivot mount not equal the
weight of the heavy end of the declination
(3) without the weight of the rod ends are not equal
distance from the fulcrum of an equal weight
hanging from the far end of the declination
(4) the role of a weight can be uniformly distributed
with a few to replace the role of weight, as long as
the center of gravity remains unchanged. Instead of
several uniform distribution of weight can be a
hanging in their center of gravity at the place of
weight
(5) similar to the graph of the distribution center is in a
similar manner starting from these axioms
• In addition, there is a conclusion that
in the "center of gravity" theory, based on the
Archimedes discovered the principle of lever, that
"two weights are balanced, they are away from the
fulcrum is inversely proportional to the distance and
weight.”
Lever of Archimedes not only stayed on the
theoretical aspects, but also carried out a
principle whereby series of inventions.
It is said that he had the help of levers and
pulleys, so parked in the beach into the water on
masts as well, in the defense of Syracuse
against the Roman naval attack in the battle, the
principle of Archimedes created a much leverage,
close of the sling, use it to shoot a variety
of missiles and stones to attack the enemy, once
outside the city the Romans arrested at Syracuse
for 3 years.
Moreover… we find the relationship
between torque and lever:
Due to the foundation of principle of leverage,
there develops another principle: the second
principle of lever.
Explanation of The Second Principle of Lever
the second principle of lever which is used in
the 3D space. There exists two torques in the
bowed lever in the process of rotating. One is
power torque, the other is magnified inner
resistance torque.
The theory of first principle of lever all comes
from the statics while the second principle of
lever is applied in the field of dynamics.
Using algebra to
express it as :
M1×r2×L1
= M2 ×r1×L2
In which: M1 is
moment torque, M2 is
resistance torque, L1 is
power arm, L2 is
resistance torque, r1 is
radius of moment
torque, r2 is radius of
the inner resistance
torque
The second principle of leverage is created to do
the problems that the first principal cannot solve.
For example: we can use the 2rd principle of leverage
to solve the hard nut called the real long-term CVT
when dealing with the mechanical transmission.
This principle establishes a contact between lever and
torque. Although it is very useful, the application of this
principle is far beyond our knowledge …
Compared with this one, the following application of lever
is much easier …
Application 2: Lever in our body
Muscles and bones act together to form levers…
as a matter of fact, laborious-power levers occupy
human body’s levers in a great measure, and the
others are equal-power and saving-power lever.
Class 1 lever: nod head
When you nod your head, the
pivot is the place where the skull
meets the top of the spine. The
lever arm is your skull. You use
your the neck muscles to
surmount the load caused
by the weight of the head
and lift your head up.
Class 2 lever: Stand on the tip toes
When you stand on your tip toes, the tip toe is the pivot
and the muscle on your heel exerts a pulling force upward,
equaling the effect of your weight’s gravity of your weight.
Since the pulling force of muscle is less than the weight,
this set is a laborious-power lever. Besides, the longer your
feet are, the less force you need to spend.
Class 3 lever: Bent Arm
During the process of lifting up heavy goods,
arm acts as the lever and elbow point is the
pivot. This set is a laborious-power lever.
Usually, people need to spend six more
strength to lift up the goods; however, it can
save the distance.
So far, we have done lots of research and found
out the amazing relationship between torque and
lever. We also use this opportunity to learn the
lever and leverage thoroughly.
That’s the end of this project…
Reference :
Wikipedia
http://en.wikipedia.org/wiki/Lever
Baidu Baike
http://baike.baidu.com/view/85069.htm
Google image
http://www.google.com/images?q=%E6%9D%A0%E6%9D%86
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h=810