Designing Simple Machines

8/10/2019 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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OutputDistance

The force

you exert

The weight


Distance


Distance

from theoutputforce to thefulcrum


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Third Class Lever

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OutputDistance

The force

you exert

The weight


Distance


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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Designing Simple Machines