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Work, Mechanical Advantage and
Efficiency
Simple Machines
Essential Question: What is the relationship between IMA & MA
All machines can be classified as or a combination of levers and inclined planes.
Manipulate the Law of Conservation of Energy
The amount of energy that goes in the machine = to the amount of energy that comes out.
Work in = Work out
Fin x d in = F out x d out
Simple Machines
Machines DO NOT decrease work!!!They change the Force and distance
needed to get a certain amount of work done.
Machines and Work
F d F d F d
Work Done
FinFout
d in= 1.75 m
d out= 0.25 m
Fulcrum/ Pivot point
2000 N
1.75 m
F in x d in = F out x d out
x = 0.25 mxFin 2000 NFin = 0.25 mx2000
N1.75 m = 286 N
How much a machine changes the force There are 4 variables
Fe = “effort force”: how much YOU put in.
Fr = “resistance force”: force generated by machine.
de = “distance effort”: distance effort must travel i.e. length of a lever’s effort arm.
dr = “distance resistance”: distance the resistance must travel i.e. the length of the resistance arm in a lever.
Mechanical Advantage
Mechanical Advantage
FeFr
d e
d r
Fulcrum/ Pivot point
Model of a machine in an “ideal” world.
No friction or heat loss.Ideal mechanical advantage = distance effort/distance resistance
IMA = de/dr
This is a ratio so there are no units
Ideal Mechanical Advantage
In the “real” world energy is lost as friction and heat.
Mechanical Advantage = resistance force/effort force
MA = Fr/Fe No units
Mechanical Advantage
Workout / Workin x 100
The ratio of a machine’s MA to its IMA determines its efficiency.
Efficiency = MA / IMA x 100.
Efficiency
3 lever typesClass 1 lever:Ex: crowbar
Levers
FeFr
d ed r
Fulcrum/ Pivot point
Label Fe = “effort force”
Fr = “resistance force”
de = “distance effort”
dr = “distance resistance”
Class 2 lever:Ex: wheel barrow
Levers
Fe
Fr
d e
d r
Fulcrum/ Pivot point
Label Fe = “effort force”
Fr = “resistance force”
de = “distance effort”
dr = “distance resistance”
Class 3 lever:Ex: bicep
Levers
Fe
Fr
d e
d r
Fulcrum/ Pivot point
Label Fe = “effort force”
Fr = “resistance force”
de = “distance effort”
dr = “distance resistance”
Example: ramp
Inclined Plane
dr
de
Fr
Fe
Inclined plane
Inclined plane wrapped around a cylinder
Lever
Variation of wheel and axle
Wedge:
Screw:
Wheel and axle:
Pulley:
More simple machines
Height = 0.5 m
Height does not change, only the angle.
Height = 0.5 m
Scale reads = 300g
Car mass = 500g
Length = 0.83 m
300
Height = 0.5 m
Scale reads = 3N
Car mass = 5N
Length = 0.83 m
300
Modified test
Height = 0.5 m
Scale reads = 300g
Car mass = 400g
Length = 0.66 m
300
Inclined Plane• Example: ramp
Forc
e
Dis
tan
ce
Dis
tan
ce
Forc
e
dr
de
Fr
Fe
Mechanical Advantage Example
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
