Machines Machines Machines Machines Machines

Machines Force Work Power Mechanical Advantage Ideal Machines 6 Simple Machines Efficiency

Machines

Machinedevice that makes work easierchanges the size and/or

direction of the exerted force

Work

A force causes an object to moveThe movement must be in the

same direction as the applied force.

Units: Nm or Joules (J)

W = F × d

Powerrate at which work is donemeasured in watts (W)

P = W

t P = power (W)

W = work (J)

t = time (s)

Calculating Power

P = W ÷ t

W = F·d

W = (450 N)(1.5 m) = 675 J

P = 675 J ÷ 3.0 s

P = 225 W

F = 450 N

d = 1.5 m

t = 3.0 s

A figure skater lifts his partner, who weighs 450 N, 1.0 m in 3.0 s. How much power is required?

Forces

Effort Force (Fe)force applied to the machine“what you do”

Resistance Force (Fr)force applied by the machine“what the machine does”

WorkWork Input (Win)

work done on a machine

Work Output (Wout)

work done by a machine

Win = Fe × de

Wout = Fr × dr

Ideal Machine EquationConservation of Energy

can never get more work out than you put in

trade-off between force and distance

Win = Wout

Fe × de = Fr × dr

Ideal Machine Equation 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?

0.3m

Fe × de = Fr × dr

(15 N) de = (150 N)(0.3m)

de = (150 N)(0.3m)

15N

de = 3.0 m

Work In an ideal machine...

But in the real world…some energy is lost as friction

Win = Wout

Win > Wout

Mechanical AdvantageMechanical Advantage (MA)

number of times a machine increases the effort force

e

r

F

FMA

MA > 1 : force is increasedMA < 1 : distance is increasedMA = 1 : only direction is changed

Mechanical Advantage A worker applies an effort force of 20 N

to open a window with a resistance force of 500 N. What is the crowbar’s MA?

GIVEN:

Fe = 20 N

Fr = 500 N

MA = ?

WORK:

MA = Fr ÷ Fe

MA = (500 N) ÷ (20 N)

MA = 25

MA

Fr

Fe

Mechanical Advantage Find the effort force needed to lift a

2000 N rock using a jack with a mechanical advantage of 10.

GIVEN:

Fe = ?

Fr = 2000 N

MA = 10

WORK:

Fe = Fr ÷ MA

Fe = (2000 N) ÷ (10)

Fe = 200 N

MA

Fr

Fe

Efficiencya measure of how completely work input is converted to work output

100%W

WEfficiency

in

out

always less than 100% due to friction

Lever

A lever is 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

Resistancearm

Effort arm

Fulcrum

Mechanical Advantage

r

e

L

LIMA

Ideal Mechanical Advantage (IMA) frictionless machine

Effort arm length

Resistancearm length

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

First Class Lever

a. can increase force, distance, or neither

b. changes direction of force

r

e

L

LIMA

Second Class Lever

r

e

L

LIMA

always increases force

Third Class Leverr

e

L

LIMA

always increases distance

Pulley

a. a grooved wheel with a rope or chain running along the groove

b. a “flexible first-class lever”

Le

Lr

IMA of a Pulley

equal to the number of supporting ropes

IMA = 0 IMA = 1 IMA = 2

Single Fixed PulleyIMA = 1

does not increase force

changes direction of force

Block and Tackle

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

Wheel and Axle

a. two wheels of different sizes that rotate together

b. a pair of “rotating levers”

IMA = radius of wheel radius of axle

IMA Problems 1. 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?

IMA = Le

Lr

IMA = (140 cm) ÷ (20 cm)

IMA = 7

IMA = ?

Lr = 20 cm

Le = 140 cm

2. 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?

IMA = ?

rw = 20 cm

ra = 5 cm

IMA = rw ÷ ra

IMA = (20 cm) ÷ (5 cm)

IMA = 4

3. 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?

rw = IMA · ra

rw = (6)(4 cm)

rw = 24 cm

ra

rw

IMA = 6

rw = ?

ra = 4 cm

Inclined Plane

h

lIMA

sloping surface used to raise objects

Inclined Plane How much force must be exerted to

push a 450 N box up a ramp that is 3 m long and 1.2 m high?

IMA = l ÷ hIMA = (3 m)÷(1.2 m)IMA = 2.5

Fe = Fr ÷ MAFe = (450 N)÷(2.5)Fe = 180 N

Fe = ?

Fr = 450 N

l = 3 m

h = 1.2 m

A worker exerts a force of 500 N to push a 1500 N sofa 4.0 m along a ramp that is 1.0 m high. What is the ramp’s efficiency?

Fe = 500 N

de = 4.0 m

Fr = 1500 N

dr = 1.0 m

Win = (500N)(4.0m) = 2000 J

Wout = (1500N)(1.0m) = 1500 J

E = 1500 J × 100% 2000 J

E = 75%4.0m4.0m

1.0m

500N

1500N

100%in

out

W

WE

Screw

inclined plane wrapped in a spiral around a cylinder

Wedgea moving inclined plane with 1 or 2 sloping sides

Rube Goldberg Machine

Rube Goldberg walks in his sleep, strolls through a cactus field in his bare feet, and screams out an idea for self-operating napkin: As you raise spoon of soup (A) to your mouth it pulls string (B), thereby jerking ladle (C) which throws cracker (D) past parrot (E). Parrot jumps after cracker and perch (F) tilts, upsetting seeds (G) into pail (H). Extra weight in pail pulls cord (I), which opens and lights automatic cigar lighter (J), setting off sky-rocket (K) which causes sickle (L) to cut string (M) and allow pendulum with attached napkin to swing back and forth thereby wiping off your chin. After the meal, substitute a harmonica for the napkin and you'll be able to entertain the guests with a little music.