How Machines Do Work:How Machines Do Work:Advantageous and Efficient Advantageous and Efficient

NotesNotes

What is a machine? What is a machine?

A machine is a device that can be used to A machine is a device that can be used to perform work easily, or in a more efficient perform work easily, or in a more efficient manner.manner.

How do machines make work How do machines make work easier? Does a machine change easier? Does a machine change

amount of work?amount of work?

By changing By changing the amount of the amount of forceforce you you exert, exert, the the distancedistance over which you over which you exert your force, exert your force, or the or the directiondirection in in which you exert the force. which you exert the force.

NO! NO! A machine does not change the A machine does not change the amount of work!amount of work!

In Summary, 3 Basic things a In Summary, 3 Basic things a machine changes are…machine changes are…

ForceForce

DistanceDistance

DirectionDirection

Input Force and DistanceInput Force and Distance

Input Force - The Input Force - The efforteffort or or force you exert on the force you exert on the machine machine Input Distance - The Input Distance - The distance you move the distance you move the machinemachine

Output force and DistanceOutput force and Distance

Output Force - The force Output Force - The force exerted by the machine on the exerted by the machine on the object object (also called (also called resistanceresistance or or the the loadload and always equal the and always equal the weightweight if the machine lifts it) if the machine lifts it)

Output Distance - The distance Output Distance - The distance the machine movesthe machine moves

Input and Output WorkInput and Output Work

Input force x input distance = input workInput force x input distance = input work

–Work done by you! (Work done by you! (II do do iinput work)nput work)

Output force x output distance = output Output force x output distance = output workwork

–Work done by the machine! (M, O)Work done by the machine! (M, O)

Output work can Output work can nevernever be greater be greater than input work!than input work!

Increasing (multiplying) a ForceIncreasing (multiplying) a Force

Input (you)Input (you)SmallSmall force force

LargeLarge distanc distancee

Output (machine)Output (machine)LargeLarge force force

SmallSmall distance distance

Input force less than output force!Input force less than output force!

Examples:Examples:RampRamp: large ramp distance (input) to lift : large ramp distance (input) to lift something up a smaller height (output something up a smaller height (output distance)distance)

Increasing (multiplying) a DistanceIncreasing (multiplying) a Distance

Input (you)Input (you)Large Large force force

SmallSmall distance distance

Output (machine)Output (machine)SmallSmall force force

LargeLarge distance distance

Input force more than output force!Input force more than output force!Input distance less than output distance!Input distance less than output distance!

Examples:Examples:Hockey stick Hockey stick (you move stick small distance, bottom of stick (you move stick small distance, bottom of stick moves large distance to hit puck)moves large distance to hit puck)ChopstickChopstick (you move hands small distance, end of sticks (you move hands small distance, end of sticks move large distance to pick up food)move large distance to pick up food)BicycleBicycle (you move legs small distance, bike moves a larger (you move legs small distance, bike moves a larger distance)distance)

FYI: A little something about FYI: A little something about force and distanceforce and distance

Think of force and distance as if they are on Think of force and distance as if they are on a see-saw – when one goes up the other a see-saw – when one goes up the other goes downgoes down

If the machine’s force (output) is less than If the machine’s force (output) is less than your force (input), then the output distance your force (input), then the output distance needs to be more than the input distanceneeds to be more than the input distance

If the machine’s force (output) is more than If the machine’s force (output) is more than your force (input), then the output distance your force (input), then the output distance needs to be less than the input distanceneeds to be less than the input distance

Changing Direction of WorkChanging Direction of Work

If a machine If a machine onlyonly changes direction: changes direction:Input and output force are the same, input Input and output force are the same, input and output distance are the sameand output distance are the sameExamples:Examples:– Weight machineWeight machine: you pull down, weight moves : you pull down, weight moves

upup– SailboatsSailboats: you pull rope down, sail goes up : you pull rope down, sail goes up

(this is a lot easier than standing on the top of (this is a lot easier than standing on the top of the mast and pulling the sail up!)the mast and pulling the sail up!)

Mechanical AdvantageMechanical Advantage

A machine’s mechanical advantage is the A machine’s mechanical advantage is the number of timesnumber of times a force exerted on a a force exerted on a machine is machine is multiplied by the machinemultiplied by the machine..

Mechanical Advantage = Mechanical Advantage = Output ForceOutput Force

Input ForceInput Force

No units for MA!No units for MA!

Let’s open a can with a can opener. If Let’s open a can with a can opener. If you exert 10 Newtons on the opener, you exert 10 Newtons on the opener, and the opener exerts a force of 30 and the opener exerts a force of 30

Newtons on the can, then what is the Newtons on the can, then what is the mechanical advantage?mechanical advantage?

MA = output F / input FMA = output F / input FMechanical Advantage = Mechanical Advantage = 30N30N

10N10NMechanical Advantage = 3Mechanical Advantage = 3The machine increased the force exerted (times The machine increased the force exerted (times 3!), so it must have decreased the distance3!), so it must have decreased the distance

Another ExampleAnother Example

The input force on a machine is 20 N and The input force on a machine is 20 N and the output force is 10 N. What is the MA?the output force is 10 N. What is the MA?

MA = output F / input FMA = output F / input F

MA = 10 N / 20 NMA = 10 N / 20 N

MA = 0.5MA = 0.5

Machine decreased force (divided by 2), Machine decreased force (divided by 2), but must have increased distance but must have increased distance

What is happening to the MA?What is happening to the MA?If MA is over 1: If MA is over 1:

Force is multiplied! (output force more Force is multiplied! (output force more than input, output distance is less)than input, output distance is less)

If MA is less than 1 If MA is less than 1

Distance is multiplied! (output force less Distance is multiplied! (output force less than input, so output distance is more)than input, so output distance is more)

If MA = 1If MA = 1

Machine only changes direction – force Machine only changes direction – force and distance are the same for input and and distance are the same for input and outputoutput

EfficiencyEfficiency

Ideally: the input work will equal the output Ideally: the input work will equal the output workwork

This does not occur in the real world This does not occur in the real world due to due to friction friction (some work needs to be used to (some work needs to be used to overcome the friction)overcome the friction)

Efficiency: compares output work to input workEfficiency: compares output work to input work– Always a percentageAlways a percentage– Higher the percentage more efficient the Higher the percentage more efficient the

machinemachine

To Calculate EfficiencyTo Calculate Efficiency

Efficiency = Efficiency = Output workOutput work x 100 x 100

Input workInput work

Let’s say you cut the lawn with a hand Let’s say you cut the lawn with a hand lawn mower. You do 250,000 Joules of lawn mower. You do 250,000 Joules of

work to move the mower. If the work work to move the mower. If the work done by the mower in cutting the lawn is done by the mower in cutting the lawn is 200,000 Joules, what is the efficiency of 200,000 Joules, what is the efficiency of

the lawn mower?the lawn mower?Efficiency = Efficiency = 200,000200,000 J X 100 J X 100

250,000 J250,000 J

Efficiency = 0.8 x 100Efficiency = 0.8 x 100

Efficiency = 80%Efficiency = 80%

Real and Ideal MachinesReal and Ideal Machines

There is no machine that is perfect; all There is no machine that is perfect; all machines have friction. The efficiency of machines have friction. The efficiency of every machine is less than 100%.every machine is less than 100%.ideal mechanical advantage (IMA):ideal mechanical advantage (IMA): The The mechanical advantage of a machine mechanical advantage of a machine without friction (100 % efficient)without friction (100 % efficient)actual mechanical advantage (AMA): actual mechanical advantage (AMA): Machine’s Machine’s measured (real life w/ friction) measured (real life w/ friction) MAMA

SummarySummary

For both MA and efficiency: out/inFor both MA and efficiency: out/in

MA: use forceMA: use force

Efficiency: use workEfficiency: use work

A little question for you…A little question for you…

You are moving a table up to the door of You are moving a table up to the door of your house. Instead of carrying the table your house. Instead of carrying the table up the front stairs, you use a ramp. You up the front stairs, you use a ramp. You put in 200 N of force to move the 30 kg put in 200 N of force to move the 30 kg table. The door is 3 m up from the ground table. The door is 3 m up from the ground and the ramp is 6 m long.and the ramp is 6 m long.

What is the mechanical advantage of the What is the mechanical advantage of the ramp?ramp?

What is the efficiency of the ramp?What is the efficiency of the ramp?

Mechanical AdvantageMechanical Advantage

Output F = 30 kg * 9.8 m/sOutput F = 30 kg * 9.8 m/s22 = 294 N = 294 N (WEIGHT)(WEIGHT)

Input F = 200 NInput F = 200 N

Mechanical Advantage = Mechanical Advantage = output Foutput F

input Finput F

MA = 294 N / 200 N MA = 294 N / 200 N

MA = 1.47MA = 1.47

EfficiencyEfficiency

Output W = output F x output D Output W = output F x output D 294 N * 3 m = 882 J (use height of 294 N * 3 m = 882 J (use height of ramp as D)ramp as D)Input W = input F x input D Input W = input F x input D 200 N * 6 m = 1200 J (use length of ramp 200 N * 6 m = 1200 J (use length of ramp as D – this is how far you move) as D – this is how far you move) E = (output W / input W) * 100E = (output W / input W) * 100Efficiency = 882 J / 1200 J = .735Efficiency = 882 J / 1200 J = .7350.735 * 100 = 73.5% efficient0.735 * 100 = 73.5% efficient

If you were to find the IMA…If you were to find the IMA…

output W = input W since machine would output W = input W since machine would be 100% efficientbe 100% efficientSo - input work would be So - input work would be 882 J 882 J not 1200 J (no not 1200 J (no friction so no extra work needed)friction so no extra work needed)

IF = IW / ID – need to find new input forceIF = IW / ID – need to find new input force

= 882 J / 6 m (882 N•m / 6 m)= 882 J / 6 m (882 N•m / 6 m)

= 147 N (new input force)= 147 N (new input force)

MA = 294 N / 147 N = MA = 294 N / 147 N = 2 = IMA2 = IMA

Another Way to Find this Ideal Another Way to Find this Ideal Mechanical Advantage for a Ramp Mechanical Advantage for a Ramp

(only a ramp)(only a ramp)

Ideal MA = Ideal MA = length of ramplength of ramp

height of rampheight of ramp

Ideal MA = 6m / 3m = Ideal MA = 6m / 3m = 22

This way is easier!!!This way is easier!!!

Now make the Magic Triangles Now make the Magic Triangles for MA & Efficiency.for MA & Efficiency.

Mechanical AdvantageMechanical Advantage

MA = Mechanical AdvantageMA = Mechanical Advantage

OF = Output force OF = Output force

IF = Input ForceIF = Input Force

MA = OF/IF (OF ÷ IF)MA = OF/IF (OF ÷ IF)

OF = MA x IFOF = MA x IF

IF = OF/MA (OF ÷ MA)IF = OF/MA (OF ÷ MA)

MA

OF

IF

EfficiencyEfficiency

OW

IW Eff

Eff = Efficiency OW = Output work IW = Input work

Eff = OW/IW (OW ÷ IW)OW = Eff x IW IW = OW/Eff (OW ÷ Eff)

Note the efficiency in magic triangle is a decimal.