# physics and physical measurement

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Physics and Physical Measurement. Topic 1.2 Measurement and Uncertainties. The S.I. system of fundamental and derived units. Standards of Measurement. SI units are those of the Système International d’Unités adopted in 1960 Used for general measurement in most countries. - PowerPoint PPT Presentation

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• Physics and Physical MeasurementTopic 1.2 Measurement and Uncertainties

• The S.I. system of fundamental and derived units

• Standards of MeasurementSI units are those of the Systme International dUnits adopted in 1960

Used for general measurement in most countries

• Fundamental QuantitiesSome quantities cannot be measured in a simpler form and for convenience they have been selected as the basic quanitities

They are termed Fundamental Quantities, Units and Symbols

• The FundamentalsLengthmetremMasskilogram kgTimesecondsElectric currentampereAThermodynamic temp KelvinKAmount of a substancemolemol

• Derived QuantitiesWhen a quantity involves the measurement of 2 or more fundamental quantities it is called a Derived Quantity

The units of these are called Derived Units

• The Derived UnitsAcceleration ms-2Angular acceleration rad s-2Momentumkgms-1 or NsOthers have specific names and symbolsForce kg ms-2 or N

• Standards of MeasurementScientists and engineers need to make accurate measurements so that they can exchange informationTo be useful a standard of measurement must beInvariant, Accessible and Reproducible

• 3 Standards (for information)The Metre :- the distance traveled by a beam of light in a vacuum over a defined time interval ( 1/299 792 458 seconds)The Kilogram :- a particular platinum-iridium cylinder kept in Sevres, FranceThe Second :- the time interval between the vibrations in the caesium atom (1 sec = time for 9 192 631 770 vibrations)

• ConversionsYou will need to be able to convert from one unit to another for the same quanitityJ to kWhJ to eVYears to secondsAnd between other systems and SI

• KWh to J1 kWh = 1kW x 1 h = 1000W x 60 x 60 s = 1000 Js-1 x 3600 s = 3600000 J = 3.6 x 106 J

• J to eV1 eV = 1.6 x 10-19 J

• SI FormatThe accepted SI format isms-1 not m/sms-2 not m/s/si.e. we use the suffix not dashes

• Uncertainity and error in measurement

• ErrorsErrors can be divided into 2 main classes

• MistakesMistakes on the part of an individual such asmisreading scalespoor arithmetic and computational skillswrongly transferring raw data to the final reportusing the wrong theory and equationsThese are a source of error but are not considered as an experimental error

• Systematic ErrorsCause a random set of measurements to be spread about a value rather than being spread about the accepted valueIt is a system or instrument value

• Systematic Errors result fromBadly made instrumentsPoorly calibrated instrumentsAn instrument having a zero error, a form of calibrationPoorly timed actionsInstrument parallax errorNote that systematic errors are not reduced by multiple readings

• Random ErrorsAre due to variations in performance of the instrument and the operatorEven when systematic errors have been allowed for, there exists error.

• Random Errors result fromVibrations and air convectionMisreadingVariation in thickness of surface being measuredUsing less sensitive instrument when a more sensitive instrument is availableHuman parallax error

• Reducing Random ErrorsRandom errors can be reduced bytaking multiple readings, and eliminating obviously erroneous resultor by averaging the range of results.

• AccuracyAccuracy is an indication of how close a measurement is to the accepted value indicated by the relative or percentage error in the measurementAn accurate experiment has a low systematic error

• PrecisionPrecision is an indication of the agreement among a number of measurements made in the same way indicated by the absolute errorA precise experiment has a low random error

• Limit of Reading and UncertaintyThe Limit of Reading of a measurement is equal to the smallest graduation of the scale of an instrument

The Degree of Uncertainty of a measurement is equal to half the limit of readinge.g. If the limit of reading is 0.1cm then the uncertainty range is 0.05cmThis is the absolute uncertainty

• Reducing the Effects of Random UncertaintiesTake multiple readings When a series of readings are taken for a measurement, then the arithmetic mean of the reading is taken as the most probable answerThe greatest deviation or residual from the mean is taken as the absolute error

• Absolute/fractional errors and percentage errorsWe use to show an error in a measurement(208 1) mm is a fairly accurate measurement(2 1) mm is highly inaccurate

• In order to compare uncertainties, use is made of absolute, fractional and percentage uncertainties. 1 mm is the absolute uncertainty1/208 is the fractional uncertainty (0.0048)0.48 % is the percentage uncertainity

• Combining uncertainties For addition and subtraction, add absolute uncertainitiesy = b-c then y dy = (b-c) (db + dc)

• Combining uncertaintiesFor multiplication and division add percentage uncertainitiesx = b x c then dx = db + dcx b c

• Combining uncertaintiesWhen using powers, multiply the percentage uncertainty by the powerz = bn then dz = n db z b

• Combining uncertaintiesIf one uncertainty is much larger than others, the approximate uncertainty in the calculated result may be taken as due to that quantity alone

• Uncertainties in graphs

• Plotting Uncertainties on GraphsPoints are plotted with a fine pencil crossUncertainty or error bars are requiredThese are short lines drawn from the plotted points parallel to the axes indicating the absolute error of measurement

• Uncertainties on a Graph

• Significant FiguresThe number of significant figures should reflect the precision of the value or of the input data to be calculatedSimple rule: For multiplication and division, the number of significant figures in a result should not exceed that of the least precise value upon which it depends

• EstimationYou need to be able to estimate values of everyday objects to one or two significant figuresAnd/or to the nearest order of magnitudee.g. Dimensions of a brickMass of an appleDuration of a heartbeatRoom temperatureSwimming Pool

• You also need to estimate the result of calculationse.g. 6.3 x 7.6/4.9= 6 x 8/5= 48/5=50/5=10(Actual answer = 9.77)

• Approaching and Solving ProblemsYou need to be able to state and explain any simplifying assumptions that you make solving problemse.g. Reasonable assumptions as to why certain quantities may be neglected or ignoredi.e. Heat loss, internal resistanceOr that behaviour is approximately linear

• Graphical TechniquesGraphs are very useful for analysing the data that is collected during investigationsGraphing is one of the most valuable tools used because

• Why Graphit gives a visual display of the relationship between two or more variablesshows which data points do not obey the relationshipgives an indication at which point a relationship ceases to be trueused to determine the constants in an equation relating two variables

• You need to be able to give a qualitative physical interpretation of a particular graphe.g. as the potential difference increases, the ionization current also increases until it reaches a maximum at..

• Plotting GraphsIndependent variables are plotted on the x-axisDependent variables are plotted on the y-axisMost graphs occur in the 1st quadrant however some may appear in all 4

• Plotting Graphs - Choice of AxisWhen you are asked to plot a graph of a against b, the first variable mentioned is plotted on the y axisGraphs should be plotted by hand

• Plotting Graphs - ScalesSize of graph should be large, to fill as much space as possiblechoose a convenient scale that is easily subdivided

• Plotting Graphs - LabelsEach axis is labeled with the name and symbol, as well as the relevant unit usedThe graph should also be given a descriptive title

• Plotting Graphs - Line of Best FitWhen choosing the line or curve it is best to use a transparent rulerPosition the ruler until it lies along an ideal lineThe line or curve does not have to pass through every pointDo not assume that all lines should pass through the originDo not do dot to dot!

• Analysing the GraphOften a relationship between variables will first produce a parabola, hyperbole or an exponential growth or decay. These can be transformed to a straight line relationshipGeneral equation for a straight line is y = mx + cy is the dependent variable, x is the independent variable, m is the gradient and c is the y-intercept

• The parameters of a function can also be obtained from the slope (m) and the intercept (c) of a straight line graph

or gradient = y / x

uphill slope is positive and downhill slope is negativeDont forget to give the units of the gradient

• Areas under GraphsThe area under a graph is a useful toole.g. on a force displacement graph the area is work (N x m = J)e.g. on a speed time graph the area is distance (ms-1 x s = m)Again, dont forget the units of the area

• Standard Graphs - linear graphsA straight line passing through the origin shows proportionalityy xy = k xWhere k is the constantof proportionalityk = rise/run

• Standard Graphs - parabolaA parabola shows that y is directly proportional to x2i.e. y x2or y = kx2where k is the constant of proportionality

• Standard Graphs - hyperbolaA hyperbola shows that y is inversely proportional to xi.e. y 1/xor y = k/xwhere k is the

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