12 13 h2_measurement_ppt
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Transcript of 12 13 h2_measurement_ppt
JJ H1/H2 Physics 2012JJ H1/H2 Physics 2012MeasurementsMeasurements
Expensive error in HistoryExpensive error in History
Entertainment TimeEntertainment Time
Learning OutcomesLearning Outcomes
Recall the following base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol).
Express derived units as products or quotients of the base units.
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unit
It defines some measurable feature of many different items. It consists of a numerical magnitude and a unit of measure.Area of the school compound, A = 5000 m2
Physical quantity magnitude
Numbers are not physical quantities. Without a unit, numbers cannot be a measure of any physical quantity.
What is a Physical QuantityWhat is a Physical Quantity 1
Types of Physical QuantitiesTypes of Physical Quantities
There are 2 types of physical quantities:
• Base (fundamental) quantities
• Derived quantities
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1.1 What is a Base Quantity1.1 What is a Base Quantity
A base quantity is
chosen and arbitrarily defined rather than being derived from a combination of other physical
quantities.
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7 chosen Base Quantities7 chosen Base QuantitiesBase Quantity Symbol SI unit
length
mass
time
electric current
temperature
amt of substance
luminous intensity*
m
kg
s
A
K
mol
cd
metre
kilogram
second
ampere
kelvin
mole
candela
* - Not in syllabus
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1.2 What is a Derived Quantity1.2 What is a Derived Quantity
A derived quantity is defined based on
combination of base quantities and has a derived unit that is the product and/or quotient of these base units.
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Derived QuantityDerived Quantity
Example
Velocity = Displacement Time
Unit of Velocity = unit of Displacement unit of Time
= m s = m s1
Base quantitiesDerived quantity
Derived unit
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Example Force = Mass x Acceleration
Since F = ma Therefore [ F ] = [ m ] x [ a ]
= kg x ms2
= kg m s2 = N (Newton)
Derived QuantityDerived Quantity 3
ExampleThe unit of Energy is Joule ( J ). Can you try expressing Joule in terms of its base units?
[ E ] = J = kg m2 s-2
Derived QuantityDerived Quantity 3
Derived QuantityDerived Quantity
Worked Example 1
(Pg 3)
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Derived QuantityDerived Quantity
Worked Example 2
(Pg 4)
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1.3 Homogeneity of equation1.3 Homogeneity of equation
An equation is An equation is homogenoushomogenous/ / dimensionally dimensionally consistentconsistent if: if:
The term has the same unitsThe term has the same units Only quantities of the same units can be Only quantities of the same units can be
added/ subtracted/ equated in an added/ subtracted/ equated in an equation.equation.
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Homogeneity TestHomogeneity Test
The units of the terms on the right hand The units of the terms on the right hand (RHS) of the equation must be (RHS) of the equation must be equalequal to the to the units of the terms on the LHS.units of the terms on the LHS.
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Beware!!!Beware!!!
The units for the various terms in an The units for the various terms in an equation are the same, it equation are the same, it does not imply does not imply that the equation is physically correct that the equation is physically correct
Why!!!Why!!! Incorrect CoefficientIncorrect Coefficient Missing termsMissing terms Extra termsExtra terms
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The base unit on the L.H.S. must be equal to the base unit of the terms on the right hand side.
Derived QuantityDerived Quantity
Worked Example 3
(Pg 5)
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Worked Example 4
(Pg 5)
Derived QuantityDerived Quantity 5
Derived QuantityDerived Quantity
Worked Example 5
(Pg 5)
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Derived QuantityDerived Quantity
Worked Example 6
(Pg 5)
e-bt/2m and the index bt/2m are numbers and hence have no unit.
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Learning OutcomesLearning Outcomes
Show an understanding of and use the conventions for labelling graph axes and table columns as set out in the ASE publication SI units, Signs, Symbols and Abbreviations, except where these have been superseded by Signs, Symbols and Systematics (The ASE Companion to 5-16 Science, 1995).
(to be covered during practical)
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Learning OutcomesLearning Outcomes
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 (), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T).
Make reasonable estimates of physical quantities included within the syllabus.
3.Prefixes3.Prefixes
Prefixes are used to simplify the writing of very large or very small orders of magnitude of physical quantities.
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Fraction/multipleFraction/multiple PrefixPrefix SymbolSymbol
1010-12-12 picopico pp
1010-9-9 nanonano nn
1010-6-6 micromicro
1010-3-3 millimilli mm
1010-2-2 centicenti cc
1010-1-1 decideci dd
101033 kilokilo kk
101066 megamega MM
101099 gigagiga GG
10101212 teratera TT
Examples:
1500 m = 1.5 x 103 m = 1.5 km
0.00077 V = 0.77 x 10-3 V = 0.77 mV
100 x 10-9 m3 = 100 x (10-3)3 m3 = 100 mm3
PrefixesPrefixes 7
Estimates of physical quantitiesEstimates of physical quantities
The following are examples of estimated values of some physical quantities:
Diameter of an atom ~ 10-10 mDiameter of a nucleus ~ 10-15 mAir pressure ~ 100 kPaWavelength of visible light ~ 500 nmResistance of a domestic lamp ~ 1000
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Worked Example 7
(Pg 7)
PrefixesPrefixes
From today onwards, you must learn to be sensitive to your surrounding.
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Learning OutcomesLearning Outcomes
Show an understanding of the distinction between systematic errors (including zero errors) and random errors.
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4. Measurements in Physics4. Measurements in Physics
Measuring any physical quantity requires a measuring instrument. The reading will always have an uncertainty.
This arises because
a) experimenter is not skilled enoughb) limitations of instruments
c) environmental fluctuations
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As a result, measurements can become unreliable if we do not use good measurement techniques.
Some common ways to minimize errors are:a) taking average of many readingsb) avoiding parallax errors
c) take readings promptly
Uncertainty in measurementsUncertainty in measurements 8
Analogue & Digital displays
Half the smallest scale division
Often when we measure a quantity with an instrument, we can make an estimate of the uncertainty with the following rule:
Estimating uncertainty Estimating uncertainty 8
5.35Reading =
Uncertainty = 0.05
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Reading =
Uncertainty =
2.28
0.005
Estimating uncertainty Estimating uncertainty
2.2
2.3
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Even when instruments with digital displays are used, there are still uncertainties in the measurements.
For example, when a digital ammeter shows 358 mA, it does not mean that the current is exactly 358 mA.
Estimating uncertainty Estimating uncertainty 8
5. Errors & Uncertainties5. Errors & Uncertainties
Errors or uncertainties fall generally into 2 categories :
Systematic errors
Random errors
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Random errors are errors without a fixed pattern, resulting in a scattering of readings about the mean value.
5.1 Random errors5.1 Random errors
xx x
x
x
xx
x
x
x
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The readings are equally likely to be higher or lower than the mean value.
Example: Measuring the diameter of a awire due to its non-uniformity
Random errorsRandom errors
Random errors are of varying sign and magnitude and cannot be eliminated. Averaging repeated readings is the best way to minimize random errors.
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Systematic errors are ones that occurs with a fixed pattern, resulting in a consistent over-estimation or underestimation of the actual value.
5.2 Systematic errors5.2 Systematic errors
xx
x
xx
xx
xx
xx
x
xx
xx
xx
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The readings are consistently higher or lower than the actual value.
Examples: zero error, wrong calibration, a clock running fast
Systematic errorsSystematic errors
Systematic errors cannot be reduced or eliminated by taking the average of repeated readings. It could be reduced by techniques such as making a mathematical correction or correcting the faulty equipment.
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Learning OutcomesLearning Outcomes
Show an understanding of the distinction between precision and accuracy.
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Measurements are often described as accurate or precise.
But in Physics, accuracy and precision have different meanings. It is possible to have
5.3 Precision and Accuracy5.3 Precision and Accuracy
precise but inaccurate measurements
accurate but not precise measurements
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No. of readings, n
Value of reading, x
Expected 9.81
Precision and AccuracyPrecision and AccuracySuppose we do an experiment to find g. Expected result is 9.81 ms-2.
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precise, not accurate
Accurate & precise
accurate but not precise
neither precise nor accurate
Precision and AccuracyPrecision and Accuracy8.63, 8.78, 8.82, 8.59, 8.74, 8.88 9.76, 9.79, 9.83, 9.85, 9.88, 9.90
9.64, 9.81, 9.95, 10.02, 9.77, 9.68 7.65, 8.92, 10.00, 9.12, 8.41, 9.45
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Who is the best shooter??Who is the best shooter??
xxxx
precise, not accurate
xxx
x
accurate & precise
x x
x x
accurate but not precise
x
xx
x
neither precise nor accurate
Mr Low Mr Tan
Mr KwokMr Phang
A set of measurements is precise if
b) there are small random errors in the measurements
a) the measurements have a small spread or scatter
PrecisionPrecision 10
A set of measurements is accurate if
b) there are small systematic errors in the measurements
a) the measurements are close to the actual value
AccuracyAccuracy 10
Learning OutcomesLearning Outcomes
Assess the uncertainty in a derived quantity by simple addition of actual, fractional or percentage uncertainties
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If we denote the uncertainty or error as P, then we write the measured quantity as
P ± P
Fractional error of P = P / P
Percentage error of P = P / P 100%
Absolute, Fractional & Percentage Absolute, Fractional & Percentage UncertaintyUncertainty 11
Worked Example 8
(Pg 11)
UncertaintyUncertainty 11
The length of a piece of paper is measured as 297 1 mm. Its width is measured as 209 1 mm.
(a) What is the fractional uncertainty in its length?(b) What is the percentage uncertainty in its length?
Note : 297 + 1 mm
Mean value
Absolute error
Worked Example 8Worked Example 8 11
Percentage uncertainty in its length =
= 0.337 %
1/ 297 100 %
Fractional uncertainty in its length = 1/ 297
= 0.00337
Worked Example 8Worked Example 8 11
Addition and Subtraction
If C = A + B
B A C
Uncertainty in derived quantityUncertainty in derived quantity
B A D If D = A - B
Suppose A and B are measured with uncertainties A and B respectively.
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Multiplication and Division
B
B
A
A
E
E
If E = A B
If F = A/B
A B
F A B
F
Uncertainty in derived quantityUncertainty in derived quantity 11
If A = Bn, then
If A = Bm Cn , then
If A = Bm / Cn , then
Uncertainty in derived quantityUncertainty in derived quantity
A Bn
A B
A B Cm n
A B C
A B Cm n
A B C
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Worked Example 9
(Pg 12)
UncertaintyUncertainty 12
UncertaintyUncertainty 13
To find the uncertainty of a quantity, always make it the subject of the given equation before finding its associated uncertainty. Answers should always be rounded off to 3 significant figures except for absolute errors, which are to be rounded up to 1 s.f. The mean value is always rounded off to the same number of decimal places of the absolute error when expressed with in scientific notation.
Worked Example 10
(Pg 12)
UncertaintyUncertainty 13
Make g the subject of the given equation before finding its associated uncertainty.
Worked Example 11
(Pg 14)
UncertaintyUncertainty 14
Worked Example 12
(Pg 14)
UncertaintyUncertainty 14
Learning OutcomesLearning Outcomes
Distinguish between scalar and vector quantities, and give examples of each. Add and subtract coplanar vectors Represent a vector as two perpendicular components.
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6. Scalars & Vectors6. Scalars & Vectors
A scalar quantityA scalar quantity isis specified by specified by its magnitude aloneits magnitude alone
AA vector quantityvector quantity isis specified by its specified by its magnitude and directionmagnitude and direction
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Examples of Scalars & VectorsExamples of Scalars & Vectors
Some examples:Some examples:
• displacement
Vectors
Scalars
• velocity• acceleration• force• momentum
• distance• speed• time• frequency• density
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Notes for VectorsNotes for VectorsNote:Note: A vector can be placed anywhere as long as A vector can be placed anywhere as long as
it keeps its it keeps its same length and directionsame length and direction..
Two vectors with the Two vectors with the same length but same length but different directionsdifferent directions are different. are different.
Direction for vectors must be given Direction for vectors must be given clearlyclearly without ambiguity.without ambiguity.
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Direction for VectorsDirection for Vectors3 different ways to give directions clearly:3 different ways to give directions clearly:
i) Compass pointse.g. due east, 75o north of west, 20o east of south
iii) X-Y planee.g. positive x-axis, 75o above the negative x-axis, 70o below the positive x-axis
ii) Bearings e.g. bearing of 090o, 345o, 160o
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i) Due East ii ) Bearing of 090
i) 75 north of west ii) Bearing of 345iii) 75 above the -ve x-axis
i) 40 south of eastii) Bearing of 130iii) 40 below the +ve x-axis
Direction for VectorsDirection for Vectors
75
40
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6.1 Additio6.1 Addition of vn of vectorsectors When vectors are added, the When vectors are added, the
result is result is NOTNOT just the sum of the just the sum of the numbers.numbers.
The The directionsdirections of the vectors of the vectors must be considered, especially must be considered, especially when they point in different when they point in different directions.directions.
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AdditioAddition of vn of vectorsectors
Triangle LawTriangle Law
Parallelogram LawParallelogram Law
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A
BB
A+B
A
B
A
B
A+B
A
B
6.2 Subtraction6.2 Subtraction of v of vectorsectors
A – B = A + (-B)A – B = A + (-B)
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- B
A
B
A
A - B
During a subtraction, the orientation of the second vector B is reversed before addition is applied
Vector addition/ subtrVector addition/ subtractionaction 16
Scale drawing
Mathematical formula
6.3 Mathematical 6.3 Mathematical requirementsrequirements 16
Worked Example 13
(Pg 17)
Mathematical RequirementMathematical Requirement 17
Adding (Calculating the resultant of vectors)Adding (Calculating the resultant of vectors)
When 2 perpendicular vectors are added, they give When 2 perpendicular vectors are added, they give a resultant as shown:a resultant as shown:
6.4 Resolution of vectors6.4 Resolution of vectors 17
V + H = R
H
V
R
ResolvingResolving
the the reverse processreverse process of vector addition. Instead of of vector addition. Instead of combining 2 vectors into one, a vector can be combining 2 vectors into one, a vector can be spilt spilt into 2 components.into 2 components.
Resolution of vectorsResolution of vectors 17
Rx
Ry
R
Rx = R cos
Ry = R sin
tan = Ry / Rx
6.5 Change in physic6.5 Change in physical quantityal quantity
Change in Physical quantity Change in Physical quantity
= Final Quantity- Initial Quantity= Final Quantity- Initial Quantity
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Scalar Change
Direction is not important
Involves just the subtraction of magnitudes
Vector Change
Both direction and magnitude is important
Involves subtraction of vectors
Worked Example 15
(Pg 18)
Change in physical quantityChange in physical quantity 17
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