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Simple MachinesSimple MachinesWork, Mechanical Advantage Work, Mechanical Advantage
and Efficiencyand Efficiency
Simple MachinesSimple Machines All machines can be classified as or a All machines can be classified as or a
combination of combination of leverslevers and and inclined planesinclined planes. .
Manipulates the Law of Conservation of EnergyManipulates the Law of Conservation of Energy
The amount of energy that goes in the machine The amount of energy that goes in the machine = to the amount of energy that comes out.= to the amount of energy that comes out.
Work Work in in = Work = Work out out
FFinin x d x d in in = F = F out out x d x d outout
Machines and WorkMachines and Work Machines DO NOT decrease work!!!Machines DO NOT decrease work!!! They change the Force and distance They change the Force and distance
needed to get a certain amount of work needed to get a certain amount of work done.done.
F d F d F d
Work DoneWork Done
FinFout
d in= 1.75 m
d out= 0.25 m
Fulcrum/ Pivot Fulcrum/ Pivot pointpoint
2000 N
1.75 m
F F inin x d x d inin = F = F outout x d x d outout
x = 0.25 mxFin 2000 NFin = 0.25 mx2000
N1.75 m = 286 N
Mechanical AdvantageMechanical Advantage
How much a machine changes the force How much a machine changes the force There are 4 variablesThere are 4 variables
FFe e = “= “effort forceeffort force”: how much YOU put in.”: how much YOU put in.
FFrr = “ = “resistance forceresistance force”: force generated by ”: force generated by machine.machine.
ddee = “ = “distance effortdistance effort”: distance effort must ”: distance effort must travel i.e. length of a lever’s effort arm.travel i.e. length of a lever’s effort arm.
ddrr = “ = “distance resistancedistance resistance”: distance the ”: distance the resistance must travel i.e. the length of the resistance must travel i.e. the length of the resistance arm in a lever.resistance arm in a lever.
Mechanical AdvantageMechanical Advantage
FeFr
d e
d r
Fulcrum/ Pivot Fulcrum/ Pivot pointpoint
Ideal Mechanical AdvantageIdeal Mechanical Advantage Model of a machine in an “ideal” Model of a machine in an “ideal”
world.world. No friction or heat loss.No friction or heat loss. Ideal mechanical advantage = Ideal mechanical advantage =
distance effort/distance resistance.distance effort/distance resistance.
IMA = dIMA = dee/d/dr r
This is a ratio so there are no unitsThis is a ratio so there are no units
Mechanical AdvantageMechanical Advantage
In the “real” world energy is In the “real” world energy is lost as friction and heat.lost as friction and heat.
Mechanical Advantage = Mechanical Advantage = resistance force/effort force resistance force/effort force
MA = FMA = Frr/F/Fee
No unitsNo units
EfficiencyEfficiencyWorkWorkout out / Work/ Workin in x 100x 100The ratio of a machine’s The ratio of a machine’s MA to its IMA determines MA to its IMA determines its efficiency. its efficiency.
Efficiency = MA / IMA x Efficiency = MA / IMA x 100.100.
LeversLevers
3 lever types3 lever types Class 1 lever:Class 1 lever: Ex: crowbarEx: crowbar
FeFr
d ed r
Fulcrum/ Pivot Fulcrum/ Pivot pointpoint
LabelLabel FFe e = “effort force”= “effort force”
FFrr = “resistance force” = “resistance force”
ddee = “distance effort” = “distance effort”
ddrr = “distance resistance” = “distance resistance”
LeversLevers
Class 2 lever:Class 2 lever: Ex: wheel barrowEx: wheel barrow
Fe
Fr
d e
d r
Fulcrum/ Pivot Fulcrum/ Pivot pointpoint
LabelLabel FFe e = “effort force”= “effort force”
FFrr = “resistance force” = “resistance force”
ddee = “distance effort” = “distance effort”
ddrr = “distance resistance” = “distance resistance”
LeversLevers
Class 3 lever:Class 3 lever: Ex: bicepEx: bicep
Fe
Fr
d e
d r
Fulcrum/ Pivot Fulcrum/ Pivot pointpoint
LabelLabel FFe e = “effort force”= “effort force”
FFrr = “resistance force” = “resistance force”
ddee = “distance effort” = “distance effort”
ddrr = “distance resistance” = “distance resistance”
Inclined PlaneInclined Plane Example: rampExample: ramp
dr
de
Fr
Fe
Inclined planeInclined plane
Inclined plane Inclined plane wrapped around a wrapped around a cylindercylinder
LeverLever
Variation of wheel Variation of wheel and axleand axle
More simple machinesMore simple machines
Wedge: Wedge:
Screw:Screw:
Wheel and Wheel and axle:axle:
Pulley:Pulley:
Height = Height = 0.5 m0.5 m
Height does not change, only the angle.Height does not change, only the angle.
Height = Height = 0.5 m0.5 m
Scale reads = 300g
Car mass = 500g
Length = Length = 0.83 m0.83 m
303000
Height = Height = 0.5 m0.5 m
Scale reads = 3N
Car mass = 5N
Length = Length = 0.83 m0.83 m
303000
Modified test
Height = Height = 0.5 m0.5 m
Scale reads = 300g
Car mass = 400g
Length = Length = 0.66 m0.66 m
303000
Inclined Plane• Example: ramp
Forc
e
Dis
tan
ce
Dis
tan
ce
Forc
e
dr
de
Fr
Fe
Mechanical Advantage Mechanical Advantage ExampleExample
200 N75N
1 m 4 m
FeFr
d ed r
500 N
Class 3 leverClass 1 lever Class 2 lever
Fe
Fr
de
dr
FeFeFe
Fr FrFr
dr
dr drde
de de
Force Resistance
Fulcrum
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