ENGINEERING STUDIES ATAR COURSE DATA BOOK 2016

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2016/34362

Engineering Studies Data Book updated January 2016

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___________________________________________________________________________________________ 2 Engineering Studies Data Book 2016

CORE CONTENT

SI units SI unit

Quantity

Name

Symbol

length

metre

m

mass

kilogram

kg

time

second

s

joule

J

watt degree Celsius square metre

W °C m2

cubic metre

m3

metre per second

m s-1

kilogram per cubic metre

kg m-3

energy, work, quantity of heat power Celsius temperature area volume speed, velocity mass density

Standard prefixes Factor

Prefix

Symbol

Factor

Prefix

Symbol

1012

tera

T

10-3

milli

m

109

giga

G

10-6

micro

μ

106

mega

M

10-9

nano

n

103

kilo

k

10-12

pico

p

Common constant Item Ratio of the circumference of a circle to its diameter

Engineering Studies Data Book 2016

Symbol

π

Value 3.14159

3

CORE CONTENT

General formulae Side lengths of a right triangular plane figure

2 h= o2 + a 2

a h o sin θ = h o tan θ = a p = πd cos θ =

Angular relationships of a right triangular figure

Perimeter of a circle [p]

h is the hypotenuse o is the opposite side a is the adjacent side

θ is the angle h is the hypotenuse o is the opposite side a is the adjacent side d is the diameter

Area of a circle [A]

A = πr 2

r is the radius

Surface area of open ended cylinder [A]

A = π dh

Volume of a cylinder [V]

V = π r 2h

d is the diameter h is the height r is the radius h is the height

Surface area of a sphere [A]

A = 4πr 2

r is the radius

Volume of a sphere [V]

V = 43 π r 3

r is the radius

Density [ρ] of a material

m V E = Pt

ρ=

Energy [E] Efficiency [η] %

η% =

Output × 100 Input

m is mass V is volume t is the time taken P is the power η is the efficiency (%)

___________________________________________________________________________________________ 4 Engineering Studies Data Book 2016

CORE CONTENT

Selected material properties Material

Density kg m

-3

Elastic (Young’s) modulus kN mm

-2

Ultimate tensile * strength N mm

Yield stress

Electrical conductivity

Thermal conductivity

N mm-2

Ω-1m-1 × 106

W m-1K-1

-2

Structural steel

7850

200

470

250

Stainless steel

7600

200

860

502

Cast iron

7200

120

180

Wrought iron

7750

200

Aluminium

2710

70

150

Brass

8740

90

Copper

8930

Zinc

13.0 1.35

46 16

10.3

80

10.3

80

95

37.7

237

190

50

16.7

109

112

210

70

59.5

401

7130

108

200

13.8

16.8

116

Solder (60% lead, 40% tin)

9280

23.7

37

-

7.28

43.6

Concrete

2400

30

40

0.8

(compressive)

Concrete (steel

0.8

reinforced)

Timber (parallel to grain)

12

105 19.7 – 80

0.16

Polypropylene

1240

4

Polycarbonate

1200

2.3

70

2.3

40

48.3

75

45

70

73.7

0.19

3600

1.05

50 000

2320

ABS plastics

50

0.13 0.19 2.34

Nylon

1160

Acrylic

1190

3.2

Glass

2500

69

Diamond

3520

1000

19 320

82

Ice

931

9.17.5@-5°C

Pure water

1000

Sea water

1022

Petrol

740

0.15

Crude oil

800

0.15

Gold

2–4

220

40 85

44.6

318 2.25@-5°C

* Unless noted as compressive strength.

Engineering Studies Data Book 2016

5

MECHANICAL

SPECIALIST FIELD

Basic formulae (Mechanical) 1 Parameter Mechanical Advantage [MA] Velocity Ratio [VR]

Velocity ratios in drive trains (for gear or pulley train ) [VR]

Formula

MA =

Fload Feffort

Fload is the output force Feffort is the input force

VR =

deffort dload

deffort is the distance moved by the

VR =

F1 F2 F3 D1 D2 D3

Torque [τ]

τ = Fr

Moment of a force [M]

M = Fd

Stress[σ] or Pressure [p] Strain [ε] Young’s (Elastic) modulus [E] Young’s (Elastic) modulus [E] expanded formula

Factor of Safety [FS]

Acceleration [a]

Velocity [v]

Distance [s]

Force [F] Equilibrium conditions

σ ( p)= ∆L L

ε= E=

F A

σ ε

FL E= A∆L FS=

σ UTS

σ safeworking

a=

v−u t

2 v= u 2 + 2as

s = ut + 12 at 2

F = ma

∑M = 0 ∑F = 0 ∑F = 0 y

x

Equilibrium conditions (expanded)

Terms

ΣCWM = ΣACWM ΣF (up ) = ΣF (down) ΣF (left ) = ΣF (right )

effort dload is the distance moved by the load F1,2 and 3 are the followers D1,2 and 3 are the drivers (measured via number of teeth on gears or by pulley diameters) F is the force r is the radius F is the force d is the perpendicular distance F is the force A is the area

ΔL is the change in length L is the original length σ is the stress ε is the strain F is the force A is the area ΔL is the change in length L is the original length

σUTS is the ultimate tensile stress σsafeworking is the safe working stress v is the final velocity u is the initial velocity t is the time u is the initial velocity a is the acceleration s is the distance u is the initial velocity t is the time a is the acceleration m is the mass a is the acceleration Σ is the ‘sum of’ M are the moments Fy are the vertical force components Fx are the horizontal force components

Σ is the ‘sum of’ CWM are clockwise moments ACWM are anticlockwise moments

___________________________________________________________________________________________ 6 Engineering Studies Data Book 2016

SPECIALIST FIELD

MECHANICAL

Basic formulae (Mechanical) 2 Parameter Work [W] Power [P]

Formula

Terms

W = Fs

F is the force s is the distance moved F is the force s is the distance t is the time taken v is the average velocity t is the time taken P is the power m is the mass g is the acceleration due to gravity h is the height m is the mass v is the velocity

P=

Fs = Fv t

E = Pt

Energy [E]

E p = mgh

Potential energy [Ep] Kinetic energy [Ek]

Ek =

Potential and kinetic energy conversion Efficiency [η] %

∆E p = ∆Ek

= η% Compound gear or pulley system [RPM] Linear velocity of a gear or pulley system [v]

1

2

mv 2

Δ is the ‘change in’

Work done in moving load × 100 Work done by the effort output RPM =

= v

input RPM VR

RPM )( 2π r ) (= 60

s t

s = 2πr

Distance around a winch drum [s]

Work done in moving load is the output Work done by the effort is the input VR is the velocity ratio RPM is the revolutions per minute

r is the radius of the gear or pulley s is the distance travelled t is the time taken r is the radius of the drum

Selected SI units SI unit Name

Symbol

Expression in terms of other SI units

force

newton

N

–

m kg s-2

pressure, stress

pascal

Pa

N m-2

m-1 kg s-2

energy, work, quantity of heat

joule

J

Nm

m2 kg s-2

power, radiant flux

watt

W

–

m2 kg s-3

Derived quantity

Expression in terms of SI base units

Common constants Item Acceleration due to gravity

Engineering Studies Data Book 2016

Symbol

g

Value 9.80 m s–2

7

MECHANICAL

SPECIALIST FIELD

Second moment of area Shape

Second moment of area about centroidal axis

Dimensions

b

Rectangle solid section (vertical)

h

I xx =

bh 3 12

DD

Circular solid section x

x

I xx =

πD 4 64

D D

I xx = Circular tube section

x

x

π ( Do4 − Di4 ) 64

Do = cylinder outside diameter Di = cylinder inside diameter

tt

___________________________________________________________________________________________ 8 Engineering Studies Data Book 2016

SPECIALIST FIELD

MECHANICAL

Simple beams Beam configuration

Maximum bending moment

F F A

B

BM max = FL at A Here F is the single vertical point load.

BM max =

FUDL= ωL

FUDL L at A 2

A

B C

FUDL= ωL

BM max =

FL 4

at C

Here F is the single vertical point load.

BM max =

FUDL L 8

y=

FL3 3EI xx

at B

Here F is the single vertical point load.

Here FUDL= ωL which is the load per unit length (ω) times the length of the beam (L)

F F

Maximum deflection (y)

y=

FUDL L3 8EI xx

at B

Here FUDL= ωL which is the load per unit length (ω) times the length of the beam (L)

y=

FL3 48 EI xx

at C

Here F is the single vertical point load.

at C

Here FUDL= ωL which is the load per unit length (ω) times the length of the beam (L)

Y=

5 FUDL L3 384 EI xx

at C

Here FUDL= ωL which is the load per unit length (ω) times the length of the beam (L)

Terms:

L Length of beam between supports

ω

FUDL F E Ixx A B C

A uniformly distributed load per unit length The product of the UDL’s applied load/unit length (ω) and the length of the beam (L) An applied vertical point load The elastic (Young’s) modulus of the material of the beam The second moment of area of the beam section The left hand end of the beam The right hand end of the beam The mid-point of the beam

Engineering Studies Data Book 2016

9

MECHATRONICS

SPECIALIST FIELD

Selected SI units

Quantity

Unit

Abbreviation

Symbol

Expression in terms of other SI units

Voltage

volt

V

V

W A-1

Current

ampere

A

I

W V-1

ohm

Ω

R

V A-1

coulomb

C

Q

As

Capacitance

farad

F

C

A s V-1

Power

watt

W

P

J s-1

Frequency

hertz

Hz

f

s-1

Resistance Charge

Prefixes Prefix

Abbreviation

Multiplier

tera

T

1012

= 1 000 000 000 000

giga

G

109

= 1 000 000 000

mega

M

106

= 1000 000

kilo

k

103

= 1000

(none)

(none)

100

=1

milli

m

10-3

= 0.001

micro

µ

10-6

= 0.000 001

nano

n

10-9

= 0.000 000 001

pico

p

10-12

= 0.000 000 000 001

___________________________________________________________________________________________ 10 Engineering Studies Data Book 2016

SPECIALIST FIELD

MECHATRONICS

Standard symbols Light dependent resistor (LDR)

Cell

NPN transistor

Thermistor

Battery

IC

Non-polarised capacitor DC Power supply unit (PSU)

Integrated circuit

Voltmeter

Polarised capacitor

Ohmmeter

Diode Fuse Light emitting diode (LED) 78XX

Ammeter

Voltage regulator Lamp (also called bulb) SPST switch DC motor SPDT switch Servo DPDT switch SPDT relay Push to make switch

Push to break switch DPDT relay Resistor

Potentiometer Unipolar stepper motor Variable resistor

Engineering Studies Data Book 2016

11

MECHATRONICS

SPECIALIST FIELD

Resistor colour codes band colour

1st band

2nd band

multiplier

0

1

Brown

± 1%

Black

tolerance band

Brown

1

1

10

Red

± 2%

Red

2

2

100

Gold

± 5%

Orange

3

3

1000

Silver

± 10%

Yellow

4

4

10 000

Green

5

5

100 000

Blue

6

6

1 000 000

Violet

7

7

Grey

8

8

White

9

9

E12 Preferred values:

10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82

Example: 4 band colour code

Electrical formula wheel

___________________________________________________________________________________________ 12 Engineering Studies Data Book 2016

SPECIALIST FIELD

MECHATRONICS

Basic formulae (Mechatronics) 1 Parameter Ohm’s law

Formula

Terms

V = IR

Power law

= P VI = I 2= R

V2 R

V is the voltage I is the current R is the resistance P is the power I is the current V is the voltage R is the resistance V is the voltage I is the current t is the time Rt is the total resistance R1, R2, … are the individual resistances Rt is the total resistance R1, R2, … are the individual resistances

Electrical energy [Ee]

Ee = VIt

Resistors in series

Rt = R1 + R2 +

Resistors in parallel

1 1 1 = + + Rt R1 R2

Kirchhoff’s first law

∑I = 0

Kirchhoff’s second law

0 ∑ ∆V =

Capacitors in parallel

C = C1 + C 2 +

Capacitors in series

1 1 1 = + + C C1 C 2

C is the total capacitance C1, C2, … are the individual capacitances

Voltage dividers

Vcc= V1 + V2

Vcc is the total voltage across the resistor pair V1 is the voltage across resistor R1 V2 is the voltage across resistor R2

V1 = Vcc

R1 R1 + R2

V2 = Vcc

R2 R1 + R2

LED in series with a resistor

Transistor current gain

Engineering Studies Data Book 2016

R=

(Vcc − VLED )

h FE =

I LED

IC IB

The sum of currents flowing toward that point is equal to the sum of currents flowing away from that point The directed sum of the electrical potential differences around a closed loop in a circuit must be zero C is the total capacitance C1, C2, … are the individual capacitances

Vcc is the total applied voltage VLED is the voltage across the LED ILED is the current through the LED R is the series resistor IC is the collector current IB is the base current

13

MECHATRONICS

SPECIALIST FIELD

Basic formulae (Mechatronics) 2 Parameter

Formula

Terms

Mechanical advantage (MA)

MA =

load effort

Velocity ratio (VR)

VR =

distance moved by effort distance moved by load

VR =

Ø follower pulley Ø driver pulley

VR =

nº teeth follower gear nº teeth driver gear

VR =

nº teeth follower gear nº teeth driver gear

Pulley belt ratio Chain and sprocket ratio Gear ratio Compound gear ratio

Worm and worm wheel ratio Rack and pinion Speed, velocity

VRT is the total

VRT = VR1 × VR2 × …..

VR = distance = velocity =

velocity ratio VR1, VR2, … are the individual velocity ratios

nº teeth worm wheel 1 nº teeth pinion × nº revolutions nº teeth per metre rack

distance time

=

(rpm)(2πr) 60 VR is the velocity ratio rpm is the revolutions per minute

input rpm output rpm = VR

SI units Quantity distance time speed, velocity

SI unit Name

Symbol

metre

m

second

s

metre per second

m s-1

___________________________________________________________________________________________ 14 Engineering Studies Data Book 2016

SPECIALIST FIELD

MECHATRONICS

Diode model

Formula

On

VD = VD,on (or VF)

Terms/diagrams

Check: ID > 0 Off

ID = 0 A Check: VD < VD,on (or VF)

Transistor model (NPN BJT)

Formula

Cut-off

IB = IC = 0 A

Terms/diagrams

Check: VBE < 0.7 V

Saturation

VBE = 0.7 V VCE = 0 V Check: IB > 0 A

IC IB

Forward-active

< β (or hFE)

VBE = 0.7 V IC = β × IB Check: IB > 0 A

VCE > 0 V Transistor current gain

Gain or β or hFE =

Engineering Studies Data Book 2016

IC IB

IC is the collector current. IB is the base current.

15

MECHATRONICS

SPECIALIST FIELD

Logic symbols with truth tables and Boolean expressions A

Q

A

Q

A

0

1

B

1

0

Q

NOT Gate

OR Gate

A B

Q

AND Gate AND Gate

A B

Q NAND Gate

A

B

0

0

Q 0

1

0

0

0 1

1 1

0 1

A

B

Q

0

0

1

1

0

1

0

1

1

1

A B

Q

NOR Gate Gate NOR

A B

1 0

Q XOR Gate

A

B

Q

0

0

0

1

0

1

0 1

1 1

1

A

B

Q

0

0

1

1

0

0

0 1

1 1

0 0

A

B

Q

0

0

0

1

0

1

0

1

1

1

1

0

1

Flow chart symbols

End of Data Booklet ___________________________________________________________________________________________ 16 Engineering Studies Data Book 2016

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ACKNOWLEDGEMENTS Electrical relationships:

Electrical formula wheel. Retrieved January, 2010, from www.sengpielaudio.com/calculatorohm.htm#top.

Published by the School Curriculum and Standards Authority of Western Australia 303 Sevenoaks Street CANNINGTON WA 6107