Engineering Studies Sample Data Book
2016
Engineering Studies Sample Data Book updated June 2016
2014/22055
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2014/16628
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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
12
tera
T
10
9
giga
G
10
6
mega
M
10
3
kilo
k
10
10
10
10
10
Prefix
Symbol
-3
milli
m
-6
micro
μ
-9
nano
n
-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 (%)
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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
-2
Yield
stress
N mm
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
-2
Electrical
conductivity
Ω m × 10
-1
-1
13.0
1.35
6
Thermal
conductivity
-1
Wm K
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
Water pure
1000
Sea water
1022
Petrol
740
0.15
Crude oil
800
0.15
Gold
-1
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]
Formula
Terms
MA =
Fload
Feffort
Fload is the output force
Feffort is the input force
VR =
deffort
dload
deffort is the distance moved by the
effort
dload is the distance moved by the
load
Velocity ratios in drive
trains
(for gear or pulley train )
[VR]
F F F
VR = 1 2 3
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
v−u
a=
t
2
v=
u 2 + 2as
s = ut + 12 at 2
F = ma
∑M = 0
∑F = 0
∑F = 0
y
x
Equilibrium conditions
(expanded)
ΣCWM = ΣACWM
ΣF (up ) = ΣF (down)
ΣF (left ) = ΣF (right )
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
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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
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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
tetra
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
-3
milli
m
10
= 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
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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
Variable resistor
Unipolar stepper motor
Potentiometer
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
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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
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14
Engineering Studies Data Book 2016
SPECIALIST FIELD
MECHATRONICS
Diode model
Formula
Terms/diagrams
On
VD = VD on (or VF)
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 (Unit 1 only)
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
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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.
Copyright
© School Curriculum and Standards Authority, 2014
This document—apart from any third party copyright material contained in it—may be freely copied, or communicated on an
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Copying or communication for any other purpose can be done only within the terms of the Copyright Act 1968 or with prior
written permission of the School Curriculum and Standards Authority. Copying or communication of any third party copyright
material can be done only within the terms of the Copyright Act 1968 or with permission of the copyright owners.
Any content in this document that has been derived from the Australian Curriculum may be used under the terms of the
Creative Commons Attribution-NonCommercial 3.0 Australia licence.
Published by the School Curriculum and Standards Authority of Western Australia
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