1.4 understanding measurement

1.4 1.4 Understanding Understanding MeasurementMeasurement

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Chapter 1 Chapter 1 Introduction To PhysicsIntroduction To Physics

Learning OutcomesLearning Outcomes

Measure physical quantities Measure physical quantities using appropriate instrumentsusing appropriate instruments

Explain : Explain : 1.1. accuracy, consistency, accuracy, consistency,

sensitivitysensitivity2.2. Types of experimental errorTypes of experimental error Use appropriate technique to Use appropriate technique to

reduce errorreduce errorwww.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

Measuring InstrumentsMeasuring Instruments

Metre RuleMetre Rule Measuring tapeMeasuring tape Micrometer Screw GaugeMicrometer Screw Gauge Vernier CalipersVernier Calipers Stop watchStop watch ThermometerThermometer AmmeterAmmeter Triple beam balanceTriple beam balance Spring balanceSpring balance

AccuracyAccuracy

How close the value of the How close the value of the measurement to the measurement to the actual actual valuevalue

ConsistencyConsistency

The consistency of a measuring instrument is its ability to register the same reading when a measurement is repeated.

SensitivitySensitivity

The instruments ability to The instruments ability to detect a small changedetect a small change in the in the quantity to be measuredquantity to be measured

Responds faster, by a larger Responds faster, by a larger extend to small variations in extend to small variations in quantity measuredquantity measured

AccuracyAccuracy

The consistency of a measuring instrument is its ability to register the same reading when a measurement is repeated.

Very Consistent : Very Consistent : readings are all the same readings are all the same

everytime measuredeverytime measured

How to measure How to measure consistency?consistency?

Calculate Relative DeviationCalculate Relative Deviation High consistency:

Smaller value of relative deviation

Deviation & Relative Deviation & Relative DeviationDeviation

A A deviationdeviation is the is the differencedifference between a between a measured valuemeasured value and and its its mean valuemean value or the or the average average valuevalue..

READINGREADINGSS

11 0.50.5

22 0.40.4

33 0.50.5

44 0.30.3

55 0.40.4

AVERAGE = 0.5 + 0.4 + 0.5+0.3+0.4

5= 0.42

1.AVERAGE2.DEVIATION3.AVERAGE DEVIATION4.RELATIVE DEVIATION : average deviation x

100% average

DEVIATION (1st Reading) = 0.42 – 0.5= 0.08

CONSISTENCY

READINGS READINGS

DeviationDeviation

11 0.50.5 0.080.08

22 0.40.4 0.020.02

33 0.50.5 0.080.08

44 0.30.3 0.120.12

55 0.40.4 0.020.02

AveragAveragee

0.420.42 0.064 = 0.060.064 = 0.06

RELATIVE DEVIATION : = average deviation x 100%

average= 0.06/0.42 x 100% = 14.29 %

4amanah until here 4amanah until here 20/0120/01

The consistency of a The consistency of a measuring instrument can be measuring instrument can be improved by:improved by:

(a) (a) eliminating parallax eliminating parallax measurement.measurement.

(b) (b) exercising greater care and exercising greater care and effort effort when taking readings.when taking readings.

(c) (c) using an instrument which is using an instrument which is not not defectivedefective

The instruments ability to The instruments ability to detect a small changedetect a small change in the in the quantity to be measuredquantity to be measured

Appropriate Appropriate InstrumentInstrument

Must have:Must have:

Appropriate Appropriate sensitivitysensitivity

Choosing Appropriate Choosing Appropriate InstrumentInstrument

Must consider Magnitude Must consider Magnitude of the quantityof the quantity

Should not exceed the Should not exceed the maximummaximum and and minimumminimum capasity of the instrumentcapasity of the instrument

The smaller the change which The smaller the change which can be measured by the can be measured by the instrument,instrument,

The more sensitive the The more sensitive the instrument isinstrument is

Narrow capillaryNarrow capillary Thin walled-bulbThin walled-bulb

How to increase the How to increase the sensitivity?sensitivity?

Errors In Errors In MeasurementsMeasurements

Two types of Two types of experimental errors:experimental errors:

1.1. Systematic errorsSystematic errors

2.2. Random errorsRandom errors

Systematic errorsSystematic errors

Systematics errorsSystematics errors

Due to Due to

1.1. the error in calibration of instrument the error in calibration of instrument which makes it defectivewhich makes it defective

2.2. Zero error* of the instrumentZero error* of the instrument

Zero error – the pointer of the Zero error – the pointer of the instrument does not return to zero instrument does not return to zero when not in usewhen not in use

Will lead to a decrease in Will lead to a decrease in accuracyaccuracy

Always occur with the same value Always occur with the same value when we measure using the same when we measure using the same instrument in the same wayinstrument in the same way

Readings taken are always larger Readings taken are always larger or always smaller than the true or always smaller than the true valuevalue

Systematics errorsSystematics errors

Can we eliminate the Can we eliminate the systematic error by systematic error by repeating the measurement repeating the measurement and averaging out the and averaging out the result? result?

No! Cannot!No! Cannot! Only can by:Only can by: calibrating or doing calibrating or doing

adjustment to the adjustment to the instrumentinstrumentwww.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

Random errorsRandom errors

Due to Due to

1.1. the carelessness of the observer the carelessness of the observer when making measurement when making measurement (parallax error)(parallax error)

2.2. Sudden change of ambient factor Sudden change of ambient factor (temperature, air circulation)(temperature, air circulation)

Will lead to a decrease in Will lead to a decrease in consistencyconsistency

accuracy

VERNIER CALLIPERSVERNIER CALLIPERS

What is the accuracy ofWhat is the accuracy ofa) main scalea) main scaleb) vernier scaleb) vernier scale

Reading = 3.2 + 0.04 = 3.24 cm

MICROMETER SCREW MICROMETER SCREW GAUGEGAUGE

What is the reading?What is the reading?www.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

Reading = Reading = 2.0 + 0.22 2.0 + 0.22 = = 2.22 mm2.22 mm

What is the reading?What is the reading?

Reading = Reading = 2.5 + 0.22 2.5 + 0.22 = = 2.72 mm2.72 mm

ZERO ERRORZERO ERROR

Zero Error Zero Error = negative= negative= - (0.10 – 0.06)= - (0.10 – 0.06)= - 0.04 cm= - 0.04 cm

Zero Error = positiveZero Error = positive

= +0.05 cm= +0.05 cm

0vernier

4 amanah until here4 amanah until here27 jan 27 jan -reading msg already-reading msg already- ze msg notyet- ze msg notyet

Zero Error = +0.04 mm Zero Error = +0.04 mm meaning that 0.04 mm meaning that 0.04 mm

must be must be substracted from all substracted from all

readings taken. readings taken.

Correct readingCorrect readingMicrometer reading -Micrometer reading -(+0.04)(+0.04)= Micrometer reading - = Micrometer reading - 0.040.04

Zero Error = -0.03 mm Zero Error = -0.03 mm meaning that 0.03 mm meaning that 0.03 mm

must be must be added to all readings added to all readings

taken. taken.

Correct readingCorrect readingMicrometer reading - (-Micrometer reading - (-0.03)0.03)= Micrometer reading + = Micrometer reading + 0.030.03

Figure shows a micrometer screw gauge used to Figure shows a micrometer screw gauge used to measure the size of an object. Determine the size measure the size of an object. Determine the size of the object if the micrometer has a zeroof the object if the micrometer has a zero

(a) +0.01 mm(a) +0.01 mm (b) -0.03 mm(b) -0.03 mm

SolutionSolution The reading of the gauge The reading of the gauge = 4.50 + 0.21 = 4.71 mm= 4.50 + 0.21 = 4.71 mm (a) Size of object =Reading- Zero Erro(a) Size of object =Reading- Zero Erro

= 4.71 – (+0.01)= 4.71 – (+0.01) = 4.70 mm= 4.70 mm

(b) Size of object = Reading – Zero (b) Size of object = Reading – Zero ErrorError

= 4.71-(-0.03)= 4.71-(-0.03) = 4.74 mm= 4.74 mm

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