Designing Simple Machines
Transcript of Designing Simple Machines
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Why We Use Machines.
Machines help us to accomplish
tasks more easily.
Machines change the amount or
direction of the forcewe must use
to accomplish a task.
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There Is a Cost!
Whenever we use a machine, the
amount of work that we must do will
be greater than if we had done thejob without the machine.
Why?
Friction
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Mechanical Advantage
Machines are rated by their Mechanical
Advantage.
Mechanical Advantage is the ratio ofhow much force is exerted by the
machine (Fo) to how much force must
be exerted on the machine (Fi).MA = Fo
Fi
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Ideal Mechanical Advantage
Ideal Mechanical Advantage is theMechanical Advantage the machine
would have if there were no energylosses due to friction.
IMA is the ratio between the inputdistance to the output distance.
IMA = dido
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Calculating MA and IMA
To calculate the MA and IMA of a
machine, you must know the input and
output forces and the input and outputdistances for that machine.
As we continue with the presentation,
please complete the table passed outby your teacher to help you organize the
information about each type of machine.
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The Lever Family
Levers
Wheel and Axle Pulleys
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First Class Lever
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Input Force Output force InputDistance
OutputDistance
The force
you exert
The weight
of the objectbeing moved
Distance
from theinput forceto thefulcrum
Distance
from theoutput forceto thefulcrum
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Second Class Lever
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Input Force Output force InputDistance
OutputDistance
The force
you exert
The weight
of the objectbeing moved
Distance
from theinput forceto thefulcrum
Distance
from theoutputforce to thefulcrum
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Third Class Lever
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Input Force Output force InputDistance
OutputDistance
The force
you exert
The weight
of the objectbeing moved
Distance
from theinput forceto thefulcrum
Distance
from theoutputforce to thefulcrum
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Wheel and
Axle
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InputForce
Outputforce
InputDistance
OutputDistance
The force
you exert
The force
exerted bythe axle orthe weight
being lifted.
The radius
of thecrank,handle, orwheel
The radius of
the axle
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PulleyThe IMA of a pulley can also
be calculated by counting the
number of ropes pulling up
on the load.
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InputForce
Output force InputDistance
OutputDistance
The forceyou exert
The weight ofthe object
being lifted
How faryou pullthe rope
How far theobject islifted
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The Inclined Plane Family
Inclined Plane
Wedge Screw
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Inclined Plane
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Input Force Outputforce
InputDistance
OutputDistance
The force
you exert topush theobject upthe ramp
The weight
of theobject
beingmoved
The length of
the incline
The height
of theincline
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Wedges
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InputForce
Output force InputDistance
OutputDistance
The force
you exertto push thewedge inor under
The weight of
the object beinglifted OR theforce to separatethe object
The
length thewedge is
pushed inor under
How far
up orapart theobjectmoves
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Screw
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InputForce
Output force Input Distance OutputDistance
The forceyou exertto turnthe screw
The forceneeded toseparate thematerial or
lift the load
Thecircumferenceof the screw(2r)
Thepitch ofthescrew
threads
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IMA versus MA
If the world was perfect and there was
no friction then:
IMA = MA and Wi= Wo
But, the world is not perfect and IMA is
always greaterthan MA. However, for
preliminary designs, we can start byassuming that IMA = MA.
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Designing a Machine
To design a machine, you need the
following information:
The type of machine that best suits thesituation.
The force that you can exert.
The output force that is needed.
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Calculate the MA of the Machine
Calculate the MA by dividing the forceyou need by what you can exert.
For example, let us say that we want tolift a rock that weighs 500 N, but canonly exert a force of 100 N. The MA ofour machine would have to be:
MA = Fo = 500 N = 5
Fi 100 N
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Choose the Machine and Calculate
IMA
Select the type of machine that is best
for the situation. In this example, I would
choose a 1stclass lever. Assume that there is no friction and that
IMA = MA. In this example, MA =5,
therefore, IMA = 5.
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Design the Machine
The IMA of a 1stclass lever is:IMA = di = Distance from the input force to the fulcrum
do Distance from the output force to thefulcrum
In this example, the IMA = 5. If I place
the fulcrum 50 cm from the rock, then
the do will equal 50 cm.
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Design the Machine
Using the formula for IMA, I cancalculate how long the lever must be
and/or how far away from the fulcrum Imust exert my force (di).
IMA = di or di= IMA x dodo
For this example
di= IMA x do = 5 x 50 cm = 250 cm
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Your Turn to Try!
You need to lift a 600 N weight using a
winch (wheel and axle). You can exert
only 75 N and the axle of the winch hasa radius of 4 cm. How long must the
handle of the winch be?
You want to push a 1000 N box up aramp to a loading dock that is 3 m off
the ground. You can only exert a force
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Efficiency
The efficiency of a simple machine is acomparison between how much work you put
into the machine versus how much you get
out.
Percent efficiency is easily calculated by
using one of the formulas below:
% Efficiency = Wo x 100 = Fo x dox 100
Wi Fi x di
OR
% Efficiency = MA x 100
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Conclusion
Remember, machines change the size
and direction of forces, but that change
comes at a cost.
The use of machines
always require morework.
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