Download Measurement, Units & Uncertainty

Properties of
Matter
Measurement
“To measure is to know”
“If you cannot measure it, you cannot improve it”
Lord Kelvin (Sir William Thomson)
Scientific Notation
• In physics, the numbers we deal with
are either very small (size of atoms) or
very large (distances in space)
• This requires a different method in
writing out our numbers
• In scientific notation, numbers are
represented through the power of
ten.
101 = 10
102 = (10x10) = 100
103 = (10x10x10) = 1000
• The distance from the earth to the
sun is 149,597,870,600 m. This can be
written as 1.496 x 1011 m
Number
Scientific Notation
1000
1 x 103
1,000,000
1 x 106
0.01
1 x 10 -2
0.000000001
1 x 10-9
Scientific Notation: Quick Tip
To write a number in scientific notation:
 Move the decimal point to create a new number
between 1 and 10
 Count the number of places the decimal point was
moved
 This is the exponent of 10
 The exponent is positive if the original number is greater than one
 The exponent is negative if the original number is less than one
Prefixes for the Power of Ten
Power
Prefix
Abbreviation
103
Kilo
k
106
Mega
M
109
Giga
G
10-3
Milli
m
10-6
Micro
μ
10-9
Nano
n
Prefixes
Measurements in Physics: SI Units
Physical Quantity
Name
Symbol
Length
metre
m
Mass
kilogram
kg
Time
second
s
Electric Current
ampere
A
kelvin
K
Luminous Intensity
candela
cd
Amount of Substance
mole
mol
Thermodynamic
Temperature
• All measurements conducted
in physics are related to seven
chosen fundamental
quantities
• This is known as the
International System of Units
or Systeme International
(abbreviated to SI).
• All other units of physical
constants (known as derived
units) can be broken down
into groups of the seven
fundamental units. For
example, speed is measured
in meters per second (m/s).
Deriving Units in Physics from the SI Units
Converting to SI Units
Miles can be converted to kilometers by multiplying by 1.61
If you were in a situation where you wanted to convert 5 miles to metres you
would proceed as follows:
1st change miles to kilometres (1mile = 1.61km)
5mile = 5 x 1.61
= 8.05 km
2nd change kilometres to metres (1km = 1000m)
8.05 km = 8.05 x 1000
= 8050 m
• Note: there are 100 centimetres in 1 meter. This makes 5 miles equal to 805,000
cm.
Distance, Speed, and Time
When discussing speed we normally refer to
kilometres per hour (km/hr). In physics, speed is
often spoken about in terms of meters per second
(m/s). It is therefore necessary to be able to convert
from one to the other.
Converting from hours to seconds
1hr = 60 min
1 min = 60 sec
1hr or 60 min = (60 x 60) = 3600 sec
Speed = Distance/time
Speed = 8050 m / 3600 s
= 2.2 m/s
Measurement in Practice
• Is measurement important?
• What do we need to be aware of
when taking measurements?
• Every measurement is inexact
• Need a statement of uncertainty to
quantify the inexactness
• How do we make measurements
accurate?
• Need to compare with a standard
• Traceability – a method of ensuring a
measurement is an accurate
representation of what it is trying to
measure by tracing back to a standard
Traceability and Measurement
Successful measurements depend on…
• Accurate instruments
• Traceability to national standards
• An understanding of uncertainty
• Application of good measurement practice
Accurate measurements enable us to…
• Maintain quality control during production process
• Comply with and enforce laws and regulations
• Undertake research and development
• Calibrate instruments and achieve traceability to a national
measurement standard
• Develop, maintain and compare national and international
measurement standards
Traceability / Calibration
• Test against a
standard of higher
accuracy
• NSAI National
Standards Authority
Ireland
• NPL National Physical
Laboratory UK
Definition of Kilogram
• Previously: Defined in
terms of a standard
kilogram
• 2019: The kilogram is
the mass of a body at rest
 whose equivalent energy
equals the energy of a
collection of photons
whose frequencies sum to
1.356392489652×1050 Hz.
Definition of a
Second
• The value of the second is
based on the frequency of
light emitted by cesium
atoms
• Shown is a cesium clock in
the National Institute of
Standards and Technology
• 1𝑠 =
9192631770
∆ν𝐶𝑠
Definition of the Meter
• The original definition of a
meter was in terms of the
Earth’s circumference
• Then changed to be based on
this platinum-iridium bar
• 2019 – new definition
• A metre = length of path
travelled by light in vacuum
during a time interval of 1s
9192631770
• 1m =
299792458
𝑐
∆ν𝐶𝑠
Traceability
What factors cause
inaccuracy?
• Environmental effects
• Inferior measuring
equipment
• Poor measuring
techniques
Method of guaranteeing a
measurement’s accuracy: unbroken
chain of reference back to national and
international standards.
The Standards Pyramid
• Primary Standards: Highest accuracy available
• Secondary Standards: Calibrated against primary standards
• Working Standards: Slip Gauges (Length); Certified Weights (Mass);
Standard Solutions, etc.
• Irish State body Responsible for Standards: National Standards Authority
Ireland (NSAI)
Working Standards
• A gauge block (gage block, Johansson gauge, slip gauge, or Jo
block) is a precision ground and lapped length measuring
standard. It is used as a reference for the setting of measuring
equipment used in machine shops, such as micrometers, sine
bars, and dial indicators (when used in an inspection role).
• Not always easy or convenient to use physical objects as
standards. Problems with absolute or global accuracy and
consistency. Ideally one would like to have Reproducible
Standards, i.e. standards that, in principle, could be generated
anywhere globally, to the required accuracy.
Uncertainty
What is uncertainty?
• Doubt that exists about the results of
any measurement
• Confidence in a measurement
• It does not matter how accurate a
measuring instrument is considered to
be, the measurement made will always
be subject to a certain amount of
uncertainty
200 cm ± 1 cm at a level of confidence
of 95%
Why does uncertainty matter?
• Good quality measurements
• Pass or failure
• Calibration certificate
• Calibration of instruments
Significant Figures
• There is an uncertainty associated with all measurements
• Uncertainty is also called experimental error
• Values are written using significant figures
• A digit is significant if it is meaningful with regard to the accuracy of the value
• Zeros may be ambiguous
• Scientific notation helps clarify the significance of any zeros
Significant Figures, Examples
Example: 0.00123
 3 significant figures
 In numbers less than 1, zeros immediately
to the right of the decimal point are not
significant
 Can also be clarified by writing in scientific
notation: 1.23 x 10-3
Example: 100
 May have 1 significant figure
 Zeros are ambiguous
 Rewrite in scientific notation
 1.00 x 102 shows 3 significant figures
Significant Figures in Calculations
Multiplication and division
• Use the full accuracy of all known
quantities when doing the computation
• At the end of the calculation, round the
answer to the number of significant figures
present in the least accurate starting
quantity
• Example: 976 x 0.000064 m =
0.062464 m ~ 0.062 m
(Due to the 2 significant figures in the 0.000064 m)
Rounding Error
• In multiple step problems,
you could round at
different steps
• Different final values may
be obtained
• These differences are the
rounding error
• Carry an extra significant
figure through
intermediate steps in the
computation and perform
the final rounding at the
very end
Significant Figures in Calculations
Addition and subtraction
• The location of the least significant digit in the answer is determined by
the location of the least significant digit in the starting quantity that is
known with the least accuracy
• Example: 4.52 + 1.2 = 5.72 ~ 5.7
(Due to the location of the significant digit in the 1.2)
Exact Numbers
• Some values are exact
• Not measured but defined
• Example, 1 min = 60 sec
• Appears to have 1 significant figure, but it is a definition
• Can be thought of as 60.00000000… seconds
• The number of significant figures in a calculation is determined by the
number of significant figures in other quantities involved