Work, Mechanical Advantage and Efficiency Essential Question: What is the relationship between IMA & MA

All machines can be classified as or a combination of levers and inclined planes. All machines can be classified as or a combination of levers and inclined planes. Manipulate the Law of Conservation of Energy Manipulate the Law of Conservation of Energy The amount of energy that goes in the machine = to the amount of energy that comes out. The amount of energy that goes in the machine = to the amount of energy that comes out. Work in = Work out Work in = Work out F in x d in = F out x d out F in x d in = F out x d out

Machines DO NOT decrease work!!! Machines DO NOT decrease work!!! They change the Force and distance needed to get a certain amount of work done. They change the Force and distance needed to get a certain amount of work done. FdFdFd

F in F out 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 m x F in 2000 N F in = 0.25 m x 2000 N 1.75 m = 286 N

How much a machine changes the force How much a machine changes the force There are 4 variables There are 4 variables F e = “effort force”: how much YOU put in. F e = “effort force”: how much YOU put in. F r = “resistance force”: force generated by machine. F r = “resistance force”: force generated by machine. d e = “distance effort”: distance effort must travel i.e. length of a lever’s effort arm. d e = “distance effort”: distance effort must travel i.e. length of a lever’s effort arm. d r = “distance resistance”: distance the resistance must travel i.e. the length of the resistance arm in a lever. d r = “distance resistance”: distance the resistance must travel i.e. the length of the resistance arm in a lever.

FeFeFeFe FrFrFrFr d e d r Fulcrum/ Pivot point

Model of a machine in an “ideal” world. Model of a machine in an “ideal” world. No friction or heat loss. No friction or heat loss. Ideal mechanical advantage = distance effort/distance resistance Ideal mechanical advantage = distance effort/distance resistance IMA = d e /d r IMA = d e /d r This is a ratio so there are no units This is a ratio so there are no units

In the “real” world energy is lost as friction and heat. In the “real” world energy is lost as friction and heat. Mechanical Advantage = resistance force/effort force Mechanical Advantage = resistance force/effort force MA = F r /F e MA = F r /F e No units No units

Work out / Work in x 100 Work out / Work in x 100 The ratio of a machine’s MA to its IMA determines its efficiency. The ratio of a machine’s MA to its IMA determines its efficiency. Efficiency = MA / IMA x 100. Efficiency = MA / IMA x 100.

3 lever types 3 lever types Class 1 lever: Class 1 lever: Ex: crowbar Ex: crowbar FeFe FrFr d e d r Fulcrum/ Pivot point  Label  F e = “effort force”  F r = “resistance force”  d e = “distance effort”  d r = “distance resistance”

Class 2 lever: Class 2 lever: Ex: wheel barrow Ex: wheel barrow FeFe FrFr d e d r Fulcrum/ Pivot point  Label  F e = “effort force”  F r = “resistance force”  d e = “distance effort”  d r = “distance resistance”

Class 3 lever: Ex: bicep Ex: bicep FeFe FrFr d e d r Fulcrum/ Pivot point  Label  F e = “effort force”  F r = “resistance force”  d e = “distance effort”  d r = “distance resistance”

Example: ramp drdr dede FrFr FeFe

Inclined plane Inclined plane wrapped around a cylinder Lever Variation of wheel and axle Wedge: Wedge: Screw: Screw: Wheel and axle: Wheel and axle: Pulley: Pulley:

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 30 0

Height = 0.5 m Scale reads = 3N Car mass = 5N Length = 0.83 m 30 0 Modified test

Height = 0.5 m Scale reads = 300g Car mass = 400g Length = 0.66 m 30 0

Inclined Plane Example: ramp Force Distance Force drdr dede FrFr FeFe

200 N 75N 1 m 4 m FeFe FrFr d e d r

500 N

Class 3 leverClass 1 leverClass 2 lever FeFe FrFr dede drdr FeFe FeFe FeFe FrFr FrFr FrFr drdr drdr drdr dede dede dede

ForceResistance Fulcrum