work, mechanical advantage and efficiency essential question: what is the relationship between ima...

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