Machines Machines Machines Machines II. The Simple Machines

Lever Pulley Wheel & Axle

Inclined Plane Screw Wedge

A. LeverLever

a bar that is free to pivot about a fixed point, or fulcrum

“Give me a place to stand and I will move the Earth.”

– Archimedes

Engraving from Mechanics Magazine, London, 1824

Effort arm

Resistancearm

Fulcrum

A. Lever Ideal Mechanical Advantage (IMA)

frictionless machine

r

e

L

LIMA

Effort arm length

Resistancearm length

Le must be greater than Lr in order to multiply the force.

A. LeverFirst Class Lever

can increase force, distance, or neither

changes direction of force

r

e

L

LIMA

A. LeverSecond Class Lever

always increases force

r

e

L

LIMA

A. LeverThird Class Levers

always increases distance

r

e

L

LIMA

B. PulleyPulley

grooved wheel with a rope or chain running along the groove

a “flexible first-class lever”

LeLr

F

B. Pulley Ideal Mechanical Advantage (IMA)

equal to the number of supporting ropes

IMA = 0 IMA = 1 IMA = 2

B. PulleyFixed Pulley

IMA = 1

does not increase force

changes direction of force

B. PulleyMovable Pulley

IMA = 2 increases forcedoesn’t change direction

B. PulleyBlock & Tackle

combination of fixed & movable pulleys increases force (IMA = 4) may or may not change direction

C. Wheel and AxleWheel and Axle

two wheels of different sizes that rotate together

a pair of “rotatinglevers”

Wheel

Axle

C. Wheel and Axle Ideal Mechanical Advantage (IMA)

effort force is usu. applied to wheel

axle moves less distance but with greater force

r

e

r

rIMA

effort radius

resistance radius

Problems You use a 160 cm plank to lift a large

rock. If the rock is 20 cm from the fulcrum, what is the plank’s IMA?

GIVEN:

Lr = 20 cm

Le = 140 cm

IMA = ?

WORK:

IMA = Le ÷ Lr

IMA = (140 cm) ÷ (20 cm)

IMA = 7

IMA

Le

Lr

20cm

160cm

Problems A crank on a pasta maker has a radius

of 20 cm. The turning shaft has a radius of 5 cm. What is the IMA of this wheel and axle?

GIVEN:

re = 20 cm

rr = 5 cm

IMA = ?

WORK:

IMA = re ÷ rr

IMA = (20 cm) ÷ (5 cm)

IMA = 4

IMA

re

rr

5 cm 20 cm

Problems A steering wheel requires a mechanical

advantage of 6. What radius does the wheel need to have if the steering column has a radius of 4 cm?

GIVEN:

IMA = 6

re = ?

rr = 4 cm

WORK:

re = IMA · rr

re = (6)(4 cm)

re = 24 cm

IMA

re

rr

rr re

Problems You need to lift a 150 N box using only

15 N of force. How long does the lever need to be if the resistance arm is 0.3m?

GIVEN:

Fr = 150 N

Fe = 15 N

Lr = 0.3 m

Le = ?

MA = 10

WORK:

Le = IMA · Lr

Le = (10)(0.3)

Le = 3 m

Total length = Le + Lr

Total length = 3.3 m IMA

Le

Lr

0.3m

?

150N

15N