Machines and Mechanical Systems

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Machines and Mechanical Systems
The daily lives of animals is filled with
attempts to obtain the necessities of life. We
have evolved and invented many different devices
to help us complete our daily tasks. A machine
is a device that helps us to do work. Each
machine is designed to help us complete a
specific task. The design needs to be carefully
considered and is usually refined and re-invented
several times over before a practical model is
developed.
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There are 6 basic simple machines. All other
machines are combinations of these basic 6
designs.
Screw
Lever
Ramp (Inclined Plane)
Wheel and Axle
Wedge
Pulley
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The lever is made with a solid bar and pivots
around a fixed point called the fulcrum. Levers
are used to move a weight or load. An effort
force is applied to the solid bar and the load
moves because the bar pivots on the fulcrum
transferring the force down the bar to the load.
There are 3 basic types of levers. They differ
by the relative locations of the load, effort
force and fulcrum.
First class levers have the fulcrum between the
load and effort force.
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Second class levers have the load between the
effort force and the fulcrum.
Third class levers have the effort force between
the load and the fulcrum.
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A ramp or inclined plane dilutes gravity.
Instead of lifting an object straight up or
lowering it straight down, the effect of gravity
is spread over a longer distance. Ramps are also
useful to make some straight lifts easily
accessible to devices that use wheels. Instead
of lifting an object straight up, it can easily
roll up the ramp.
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A wedge is a device that is pushed between
objects to spread them apart.
The head of this axe is a wedge. All together,
the axe is made of a third class lever with a
wedge connected at the end.
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The screw is a cylinder with a spiral groove
traveling up the outside. This device, called an
Archimedes screw, uses the unique shape of the
screw to transport water to higher locations.
Turning the screw in the correct direction lifts
the water in a straight line up the column. All
screws transform rotational motion into linear
(straight line) motion.
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A pulley uses a rope moving in a grooved wheel.
Pulleys are used to change the direction that
forces are applied and can even reduce pulling
forces.
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A wheel and axle uses two connected cylinders
that turn together.
Wheels and axles are common. However, we can
also get mechanical advantages using wheel and
axles.
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All other machines are combinations or variations
on these 6 simple designs. Our body is full or
different levers of all three classes. Combining
these six devices makes complex machines. Even
something as simple as an axe, a combination of a
lever and a wedge, is a complex machine. You may
ask why we made machines at all in the first
place. This is easy to see when we consider what
an axe does. Imaging trying to tear apart blocks
of wood with your bare hands. It is possible but
requires great effort and relatively small wood
pieces. An axe allows use to split larger pieces
of wood with less effort.
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We use machines to gain a mechanical advantage.
A mechanical advantage is the result of using a
machine to complete a task more easily. In order
to analyze mechanical advantage we need to recall
a few definitions. A force is the result of
accelerating a mass. Force is measured in units
called Newtons (N). One Newton of force is about
the same as the force you feel when you hold a
100g object. If we apply a force on an object
over a distance, we are doing work. This is the
scientific definition of work. Throwing a
football is considered work but studying science
is not considered work. Work is measured in
Joules (J). When you apply 1N of force over a
distance of 1m you have done 1J of work.
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By our definitions we get the following formula
for work.
If you weigh 650N (about 65kg) and wanted to jump
0.8 meters in the air, then to calculate your
work done you use the formula.
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The key to remember is that energy (work) can
never be destroyed. It can only be transferred.
When you move one end of a lever, the energy you
put in, is transferred to the other end of the
lever.
1.5m
1.5m
For this class 1 lever, where the fulcrum is in
the center of the load and the effort force, 10N
of force are required to hold the 10N load at the
height of 60cm.
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1.5m
1.5m
If I increase the force for a brief period and
then return back to 10N, I can raise the load.
Using our work formula we can calculate the work
done to lift the 10N load 30cm.
It takes 3 J of energy to lift this weight 30cm.
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No matter how the lifting is done, it takes 3J of
energy to lift this weight 30cm. If I change the
lever so that the fulcrum is closer to the load.
In this case, I moved the fulcrum so that the
distance from the load to the fulcrum is half the
distance from the effort force to the fulcrum.
With this lever, I only need half as much effort
force to hold the 10N load.
2m
1m
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1m
2m
To lift the load 30cm I still need to use 3J of
work. However, I have to move the left side of
the lever twice as far as before (60cm). Im
doing the same amount of work, but over a longer
distance. This means I need half as much force
as I did before. This demonstrates the force
versus distance tradeoff in mechanical advantage.
The second lever allows me to use half as much
force but I have to move it twice as far.
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We can calculate mechanical advantage using a
ratio formula.
Mechanical advantage will not have any units. It
is simply a ratio that tells you relatively how
much force is required to move a load.
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We can calculate the mechanical advantage of this
lever.
2m
1m
For every Newton of force we put into this lever,
we get twice as many out.
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0.5m
2.5m
This lever requires me to use 50N of force to
hold a 10N load.
This means I get 0.2N of output for every Newton
of input.
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0.5m
2.5m
If this lever give me only 0.2N of output for
every Newton of input how can I say the machine
gives me a mechanical advantage? The advantage is
that I only need to move the left side 6cm to
make the right side move 30cm. Remember, there
is a force versus distance tradeoff. This lever
might require a large effort force but the load
moves a large distance.
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Levers arent the only machines that give us a
mechanical advantage.
6m
3m
3m
7.5N
15N
This ramp on the right would require only half as
much force to move the ball up to the platform
however, it would have to move twice as far.
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A system of pulleys like a block and tackle can
also be used to gain a mechanical advantage. The
diagram below shows how the force is transferred
over four ropes. The same force versus distance
tradeoff occurs. It takes 25N to hold the 100N
block but 4m of rope need to be pulled in to move
the block 1m.
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Suppose we look at this wheel and axle straight
from the front. We would see two concentric
circles. In this case, the circumference of the
wheel is 30cm and the circumference of the axle
is 5cm.
The mechanical advantage of this wheel and axle
is 6. This means only 10.5N of force is needed
to hold a 90N load but the wheel must turn 6
times (a total distance of 180cm) to move the
load 30cm.
10.5N effort force
90N load force
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We have already seen the transfer of force and
energy in a machine to a load. Within a complex
machine, it may be necessary to transfer energy
many times. One way to transfer energy is by
using gears. Gears are toothy wheels that mesh
together. The interlocked teeth push on each
other as they rotate around.
The meshed gears turn each other in opposite
directions. Mechanical advantages can be
calculated using these gears similarly to a wheel
and axle.
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The gear train shows how many gears can be
interconnected. In this case, the small gear on
the right is the one where the effort force is
being applied. Therefore, the small gear is
called the driving gear (or driver). The large
gear is transferring the force to the third gear
on the bottom. Since the other two gears are
moved by the driving gear, they are called driven
gears (or follower). At each gear connection,
the direction of the turn is reversed.
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You may think that a gear train is a different
type of machine. However, a gear train is
actually a collection of first class levers.
For this gear system try to calculate the
mechanical advantage.
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Special gears with long teeth can be connected
with a chain. These are called sprockets and are
common to most bicycles. They work the same way
as gears except that the direction is NOT
reversed.
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Energy and Efficiency
There are many forms of energy. When you lift an
object in the air, it has potential energy. The
energy is potential because it could move if
released. If the load is moving, it has kinetic
energy. When a lever moves a load a distance we
have already seen that we can calculate the work
done using the formula.
When work is done, energy is transferred from one
form to another. Remember, energy can never be
created or destroyed, only changed from one form
to another.
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When energy is converted from one form to another
or if the energy moves locations, we say that
there was an energy transmission.
The engine in this car converts chemical
potential energy in the gasoline to kinetic
energy that is transferred to the wheels. There
are many steps to this transference process.
There is a problem with energy transmission. It
isnt perfect. Not all of the energy from the
gasoline is used to make the car race down the
track. Some of the energy is converted to other
less useful forms.
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In the case of a car, energy is converted to
kinetic energy and heat. In fact, most of the
energy is converted to heat. Heat is another
form of energy that is usually not useful. Heat
also dissipates into the air and is lost to us.
Therefore, we usually call heat energy that is
lost. A machine that loses very little of its
energy to heat is said to have a high efficiency.
We can calculate efficiency.
Notice that efficiency is written as a
percentage. Most cars are about 20 efficient.
This means only 20 of the energy from the
gasoline becomes kinetic energy.
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No machine is 100 efficient. There is always
some heat lost. Heat is created due to friction.
Friction is a type of interference for energy.
For example, friction can take the kinetic energy
of your moving hands and slow it down. Part of
the kinetic energy is transferred to heat. This
is why rubbing your hands together can warm them
up.
Decreasing the friction in a machine, like a
bicycle, will make it more efficient. The chain
grease on a bicycle attempts to reduce friction.
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Not all friction is bad. A bicycle needs
friction between the tires and the ground so that
it can stop. Without friction the bicycle would
continue to slide uncontrollably. Surfaces like
ice offer very little friction. This make it
very difficult for us to control ourselves when
we walk on it.
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Pressure
We live with pressure all around us. We saw that
pressure is a force acting over a certain area.
So we can get a formula for pressure.
We should also remember that pressure is measured
in pascals or pa.
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Pressure can be very useful to us due to Pascals
Law. Pascals Law states that when pressure is
exerted on a contained fluid, that pressure is
transmitted throughout the fluid equally in all
directions.
This law only works when the fluid is contained
in a tight container. This means nothing can
enter or leave the container. This is why we
call these tight containers closed systems It is
because of Pascals Law that we were able to make
hydraulic systems. A hydraulic system is a
machine that uses a fluid and pressurein a closed
system to do work.
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This hydraulic lift is an example of a machine
that uses pressure and Pascals Law to our
advantage. Lets say the surface area of the
left piston is 1m2 and the area or the right
piston is 10m2. Now, if we drop a force of 30N
on the left side we should be able to calculate
the force on the right side. We need to only
remember Pascals Law.
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To summarize, 30N of force went into the left
side and 300N of force came out the right side.
The difference is the same for any machineforce
v. distance. The right side produces ten times
the force but moves only one tenth as far as the
right side. This means that the work done on both
sides is still equal. On the left, there is less
force but greater distance. On the right, more
force but less distance. The law of conservation
of energy still holds true. Still, this allows
us to lift very heavy masses using only a small
mass.
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Closed systems can be difficult to create and
maintain. Any small leak in a hydraulic and the
machine will not function. A Pneumatic system
works in the same way as a hydraulic except, high
pressure air is pushed through a system that is
not closed.
A nailgun with a compressor uses bursts of
compressed air to force nails into wood. The air
is not in a closed system.
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An air hockey table is another pneumatic device.
It forces air out tiny holes in the surface of
the table and make the puck almost float on the
table. This reduces the friction between the
puck and the table making the puck glide much
easier over the table.
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Your body uses a hydraulic system to move blood
through your body. Your heart beats creating
pressure in the arteries and blood moves through
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When the heart pumps, blood becomes under
pressure. Pascals Law would tell us that the
blood would flow in all directions equally.
Valves opening and closing control the flow of
blood so that energy is not wasted pumping blood
backward.
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Most machines that we use today are not just
simple levers, ramps, pulleys, wheels and axles,
screws, or wedges. Most machines use a
combination of these to complete their designed
task. Each simple machine that is part of a more
complex machine is called a subsystem.
One of our most important inventions was the
steam engine. In the train, a steam engine was
fueled by burning coal. The fire was used to
vaporize steam and push it through a piston
engine that uses valves to create motion.
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The high pressure steam would increase the
pressure in the left chamber and force it open.
The piston would be pushed right, when this
happens, the pressure is reduced in the left
side, increasing the pressure in the right side.
That forces open the right side pushing the
piston back. The whole cycle repeats pushing the
piston back and forth.
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The cars internal combustion engine works in a
similar way. Instead of using steam however, the
car uses the explosive power of gasoline to drive
the piston. Cars use a 4-cycle engine.
Gasoline and air enter the engine on the
induction stroke or intake stroke. The
mixture is compressed on the compression
stroke. The spark plug ignites the fuel
starting the power stroke (this is actually
what provides the energy). The vapors are pushed
out in the exhaust stroke. These are the
4-cycles.
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Valves control the gasoline and air coming in and
the exhaust vapors out. A timing belt controls
the timing of when each valve needs to open and
close.
Intake valve
Timing belt
Exhaust valve
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The 4-cycle engine is about 20 efficient. The
less efficient but simpler 2-cycle engine is
common in small gasoline powered devices like
lawn mowers. Gasoline and air enter the piston,
the spark plug ignites the mixture and fumes are
released out a vent. While fumes are released
out, new gasoline and air come in. The causes
less efficient burning and more wasted fuel
making the 2-cycle engine less efficient than the
4-cycle counterpart.
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The internal combustion engine uses a crankshaft
to change the up and down motion into rotary
motion. A series of connecting gears then
transfer this power through the transmission and
to the wheels.
The turning motion of the motor continually
pushes and pulls gasoline and exhaust running the
engine. As long as there is fuel to burn the
engine should continue running. When the engine
is at rest, a small electric starter motor is
used to begin the cycling.
Crankshaft
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