1. Physical quantities and units Content
Learning outcomes
1.2 SI Units
(a) Show an understanding that all physical quantities
1.1 Physical quantities 1.3 The Avogadro constant 1.4 Scalars and vectors
Candidates should be able to: consist of a numerical magnitude and a unit (b) Recall the following SI base quantities and their units:
mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)
(c) Express derived units as products or quotients of the SI base units and use the named units listed in this syllabus as appropriate
(d) Use SI base units to check the homogeneity of physical equations (e) Show an understanding of and use the conventions for labelling graph axes and table columns as set out in the ASE publication Signs, Symbols and Systematics (The ASE Companion to 16–19 Science, 2000) (f) Use the following prefixes and their symbols to indicate decimal sub- multiples or multiples of both base and derived units: pico (p), nano (n), micro (µ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T) (g) Make reasonable estimates of physical quantities included within the syllabus (h) Show an understanding that the Avogadro constant is the number of atoms in 0.012 kg of carbon-12 (i) Use molar quantities where one mole of any substance is the amount containing a number of particles equal to the Avogadro constant (j) Distinguish between scalar and vector quantities and give examples of each (k) Add and subtract coplanar vectors (l) Represent a vector as two perpendicular components
Physical Quantities & Units •
Physical quantities à Physical properties that can be measured and quantified
•
All physical quantities are represented by a
Length = 100 m
numerical magnitude (value) and a unit
International System of Units (SI Units)
physical
numerical
quantity
magnitude
unit
What?
French Metric System
Why?
More systematic. Its denominations are in steps of 10, which makes it easier and more convenient to use
Importance? A standard system for international communication and exchange of data especially in scientific research, trades, etc. Examples of
Ø M.K.S System ; metre-kilogram-second
System of
Ø C.G.S System ; centimetre-gram-second
Units
Ø F.P.S System ; foot-pound-second
Base Quantity ⇒ Fundamental quantities that can’t be simplified ⇒ Base Unit: fundamental units that can’t be simplified Base Quantity
Symbol
Base Unit
Base Symbol
Length
l
metre
m
Mass
m
kilogram
kg
Time
t
second
s
Current
I
ampere
A
Temperature
T/θ
kelvin
K
Amount of Substance
n
mole
mol
Luminous Intensity
l
candela
cd
Derived Quantity Derived Quantity
Symbol
Equation
Formula
Derived Unit
Area
A
Length x Breadth
A=L
m
Volume
V
Length x Breadth x Width
V=L
m
Density
ρ
Mass / Volume
ρ = m/V
kgm
Velocity
v
Length / Time
v = L/t
ms
Acceleration
a
Velocity change / Time
a = Δ∆v/t
ms
2
3
2
3 -3
-1
-2
Some derived quantities and units have special SI names. Derived Quantity
Equation
Base Units
Secondary Unit
Symbol
Force (F)
F = ma
kgms
newton
N
Work (W) , Energy (E)
W = Fd
kgm s
joule
J
Power (P)
P = W/t
kgm s
watt
W
Pressure (p)
p = F/A
kgm s
pascal
Pa
Frequency (f)
f = 1/t
s
hertz
Hz
Charge (Q)
Q = It
As
coulomb
C
Momentum (p)
p = Ft
kgms
-
Ns
Angle
-
-
radian
rad
Potential Difference (V)
V = W/Q
kgm s A
volt
V
Resistance (R)
R = V/I
kgm s A
ohm
ΩΩ
Magnetic Flux (Φ)
Φ = FA/Qv
kgm s A
weber
Wb
-2
2 -2
2 -3 -1 -2 -1
-1
-2 -3 -1
-2 -3 -2 2 -2 -1
Prefixes Syllabus
Prefix
Symbol
Factor
Yotta
Y
10
Zetta
Z
10
Exa
E
10
Peta
P
10
✓
Tera
T
10
✓
Giga
G
10
✓
Mega
M
10
✓
kilo
k
10
✓
hecto
h
10
✓
deca
da
10
✓
deci
d
10
✓
centi
c
10
✓
milli
m
10
✓
micro
µ
10
✓
nano
n
10
✓
pico
p
10
femto
f
10
atto
a
10
zepto
z
10
yocto
y
10
24 21
18
15 12 9
6
3 2 1
-1
-2
-3 -6 -9
-12
-15 -18 -21
-24
Estimation
When making an estimate, it is only reasonable to give the figure to 1 or at most 2
decimal number since an estimate is not very precise. Physical Quantity
Reasonable Estimate
Mass of a apple
100 g / 0.1 kg
Weight of an adult
600 N
Volume of a small bean
0.5 cm
Height of a room in a house
2.5 m
Length of a football field
100 m
Temperature of the human body
37 ˚C / 310 K
Speed of a cruising jumbo jet
700 kmh
Reaction time of a young man
0.2 s
Power of a hair dryer
1000 W
Wavelength of visible light
400 nm
3
-1
•
Occasionally, students are asked to estimate the area under a graph.
•
Often, when making an estimate, a formula and a simple calculation may be involved.
•
E.g. Estimate the average running speed of a typical 17-year-olds 2.4-km run Velocity = distance / time = 2400 / (12.5 x 60) = 3.2 ≈ 3 ms
•
-1
E.g. Which estimate is realistic? Option
A
The kinetic energy of a bus travelling on an expressway is 30 000 J
B
The power of a domestic light is 300 W
©
The volume of air in a car tyre is 0.03 m3
D
The temperature of a hot oven is 300 K
Explanation A bus of mass m travelling on an expressway will travel between 50 to 80 kmh-1, which is 13.8 to 22.2 ms-1. Thus, its KE will be approximately 1⁄2 m (182) = 162 m. Thus, for its KE to be 30 000J: 162m = 30 000. Thus, m = 185kg, which is an absurd weight for a bus; ie. This is not a realistic estimate. A single light bulb in the house usually runs at about 20 W to 60 W. Thus, a domestic light is unlikely to run at more than 200W; this estimate is rather high. Estimating the width of a tyre, t , is 15 cm or 0.15 m, and estimating R to be 40 cm and r to be 30 cm, volume of air in a car tyre is = π(R 2 – r 2)t = π(0.42 – 0.32)(0.15) = 0.033 m3 ≈ 0.03 m3 (to one sig. fig.) 300K = 27 ºC. Not very hot.
Homogenous Equation •
Homogenous equation have the same units for left-hand side and right-hand side of the equation
• •
Physical equation must be homogenous to be correct
If an equation is homogenous, it is possibly true because we can’t verify the correctness of the coefficient
•
2
2
E.g. Show that the equation v = u + 2as is homogenous 2
2
v = u + 2as
-1 2
-1 2
-2
(ms )
= (ms ) + (ms )(m)
m s
=m s
m s
=m s
2 -2
2 -2
2 -2
2 -2
2 -2
+m s
# (shown)
Mole à One mole of any substance is the amount containing a number of particles equal to the Avogadro constant
Avogadro Constant à the number of atoms in 0.012 kg of carbon-12 23
à 6.02 x 10
mol
-1
Molar mass àThe mass in grams numerically equivalent to the sum of the atomic masses of the atoms in the molecular formula. Scalars
Vectors A vector quantity has both magnitude and
A scalar quantity has a magnitude only. It Definition
direction. It can be described by an arrow
is completely described by a certain number
whose length represents the magnitude of the
and a unit.
vector and the arrow-head represents the
direction of the vector.
Mass, Temperature, Time, Length, Speed, Energy, Distance, Work Done, Kinetic Energy, Pressure, Power, Electric Charge,
Examples
Volume, Density, Heat Capacity, Latent
Displacement, Force, Velocity, Angular
Heat, Frequency, Wavelength, Potential
Velocity, Acceleration, Momentum,
Difference, etc.
Displacement, Moment of Force, Torque,
Common Error:
Students tend to associate kinetic energy and pressure with vectors because of the vector components involved. However, such considerations have no bearings on whether the quantity is a vector or scalar.
Electric Field, Gravitational Field, Magnetic Field, Weight, Area, etc.
