Lesson 3 - Understanding Measurements

8/3/2019 Lesson 3 - Understanding Measurements

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Introduction

The characteristics which areemphasized in the selection of ameasuring instrument includeprecision , accuracy and sensitivity.

The meaning of Precision, Accuracy and Sensitivity.

Precision is the degree of uniformity or

reproducibility of themeasurements.

ORPrecision is the degree of a

measuringinstrument to record consistent

reading foreach measurement by the same

way.

When we say the measurementsare consistent,

we mean that all the values of themeasurements are close together.

Accuracy is the degree of closeness of the measurements tothe actual or accepted value.

When we say the measurementsare accurate,

we are actually saying that thevalues of the

measurements are close to thetrue or

accepeted value. The diagram shows the result forfour shooters A, B , C and D in atournament. Every shooters shotfive times .

The table shows the conclusion .Shooter Precision Accuracy

A High LowB Low HighC High HighD Low Low

Sensitivity of a measuringinstrument is defined as the capability

of that instrument to respond tophysical stimuli or to register smallphysical amount or differences.ORSensitivity is the degree of ameasuring instrument to record smallchange in its reading.

The smallest scale division on themeasuring instruments shows thesensitivity of the instruments. Thusthe more sensitive the measuringinstruments the finer the scaledivisions.

A vernier calipers is more sensitivethan a ruler ora miliammeter is more sensitive thanan ammeter.A sensitive instrument is not alwaysan accurate instrument.

Errors

Any measurement of a physicalquantity has errors or uncertainty.

There are two types of errors.(a) Systematic errors(b) Random errors

Systematic errors

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LESSON 3Precision(consistency )and Accuracy



Systematic errors are errors in themeasurement of a physical quantitydue to instruments, the effects of surrounding conditions and physicalconstraints of the observer.

The main characteristic of systematic

error is that its magnitude is almostconstant or appears in one directiononly. The value of the measurement isalways greater or is always less thanthe actual value.

Sources of systematic errors are:(i) Zero errors or end errors

Zero errors occurs when theinstrument gives a non- zeroreading when in fact the actualreading is zero.

(ii) Personal error of the observer.Physical constraints or limitationsof the observer can causesystematic errors.An example is the reaction time.

(iii) Errors due to instruments The examples are;A stopwatch which is faster thannormal would give readings whichare always larger than the actualtime.A thermometer which is used

under different conditions fromwhich it was calibrated.A voltmeter manufactured inGermany had been calibaratedunder different temperature andearth’s magnetic field fromMalaysia where the voltmeter isused.

(iv) Errors due to wrong assumption.For example, we assumed thatthe value of the acceleration dueto gravity g is 9.81 ms-2, but theactual value may 9.79 ms-2. Hencethere is a positive error of 0.02 ms-

2.

Systematic errors cannot be reducedor eliminated by taking repeatedreadings using the same method, the

same instrument or by the sameobserver.Systematic erros can be elimated orreduced by improving the procedureof taking the measurements , using adifferent instrument or getting

somebody else to make the themeasurements.For example for the zero errors can beeliminated by subtracting the zeroreading from the obtained readings.

Random errors

The main source of random error isthe observer or has non -constant sizeof error and is unpredictable.

The characteristics of random errors

are:(i) it can be positive or negative.

The obtained readings may begreater or less than the actualvalue.

(ii) its magnitude is not constant.Examples of random errors are:

(i) Parallax errors – occur whenthe position of the eye is notperpendicular to the scale.

(ii) Different pressures areapplied when closing the gap

of the micrometer screwgauge when it is used tomeasure the diameter of awire.

(iii) Changes in the temperatureduring an experiment.

(iv) Recording the wrong reading.(v) Mistake in counting

To eliminate or reduce randomerrors , repeated reading aretaken.

Measurement Length

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We normally use ruler, measuring tape, vernier calipers or micrometer screwgauge to measure length.

Measuring

instrumen

t

Smallest scaledivision

Ruler 0.1 cm or1 mm

Verniercalipers

0.01cm

Mikrometer

screwgauge

0.01 mm

Vernier calipers

A pair of vernier calipers can be used

to measure thickness of a wire ,internal and external diameter of abeaker, depths of a test tube ,etc.

The inside jaws are used to measureinternal diameters and the outside

jaws are used to measure externaldiameters and thickness.

The tail is used to measure depths. The main scale is marked in divisionsof 0.1 cm , while the vernier scale ismarked in divisions of 0.01 cm.

The following steps shows how to readthe vernier calipers.• Read the main scale marking

just before the zero marking onthe vernier scale.

• Find the vernier scale markingwhich joins the main scalemarking.

• The reading for a vernier scaleis always recorded in cm withtwo decimal places(The accuracy is 0.01 cm)

Example 1

Write down the reading of thefollowing vernier calipers.

Solution

Example 2

Based on the following diagrams writedown the actual thickness of theobjects.

Solution

Mikrometer screw gauge

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The micrometer screw gauge is usedto measure thickness and diameters of very small objects.

The main scale is marked in divisionsof 0.5 mm , while the vernier scale ismarked in divisions of 0.01 mm.

The jaws tigh the object that is to bemeasured.

The thimble is turned until its jawtouches the object. The ratchet knob preventsovertightening by making a clicksound when the micrometer is readyto be read.

The following steps shows how to readthe micrometer screw gauge.Read the main scale marking just

before the zero marking on the vernierscale.

•

Read the main scale marking just before the zero markingbeforev the thimble.

• Find the vernier scale markingwhich joins the main scale.

• The reading for a micrometerscrew gauge is always recordedin mm with two decimal places(The accuracy is 0.01 cm)

Example 3Write down the reading of the

following diagrams.

Solution

Example 4Based on the following diagrams writedown the actual diameters of theobjects(a)

(b)

Solution

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Measurement Mass

Accuracy :……………………………………..Reading :…………………………………….

Accuracy :……………………………………..Reading :…………………………………….

Triple beam balance

Accuracy :………………………………………….

Measurement Time

Mechanical stop watch

Accuracy :……………………………………..

Electronic stop watch

Accuracy :……………………………………

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Reading :…………………………………….

Measurement Current

Ammeter range 0 – 5AAccuracy :…………………………………………….

Double-scale ammeter

Accuracy of upper scale :……………………..Acuracy of lower scale :……………………….

Reading :………………………………………..

Miliammeter range 0- 50 mA

Accuracy:……………………………………………Reading :…………………………………………..

Accuracy:

………………………………………

Measurement Temperature

Accuracy:…………………………………………..

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TUTORI



1 The ability of an instrument givesconsistent reading , whenrepeated readings are taken iscalled as

A accuracy B

precisionC sensitivity D error

2 Which of the following should bethe small value ,so that theprecision becomes high?

A Actual value B MeanC Relative error D

Relativedeviation

3 The ability of an instrument todetect a slight change that occursin the measured quantity is calledas

A precision Baccuracy

C sensitivity D error

4 The accuracy of an instrumentincreases if

A the number of significantfigures increases

B the relative deviation relativeincreases

C the relative error increases

5 Based on the table below, whatare the measuring instruments J, K and L?

Measuringinstruments

Measurement

J 2.52 ±0.01cm

K 15.2±0.1 cmL 125.4±0.1 g

J K LA Micrometer VernierSpring

screw gauge calipersbalanceB Micrometer Vernier Triple

beamScrew gauge calipers

balance

C Vernier Metre Triplebeam

calipers rulerbalance

6 Which of the following is true?

A The parallax error is not

effected to the accuracyB The accurate instrument isalso the

sensitive instrumentC The accuracy increases when

the measurement nearest toactual value.

7 Which of the following is true?

A A stop watch is more sensitivethan an

electronicB An ammeter is more sensitive

than a galvanometerC A vernier calipers is moresensitive

than a metre rulerD A thinner-walled bulb

thermometer is more sensitivethan a thicker –walled bulbthermometer

8 Which of the following is mostlikely to show a precise shooting?

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9 Which of the following is mostlikely to show an accurateshooting but not so presicely?

10 It take 5.01 s for an object to moveto a certain distance. When anelectronic watch is used the time isrecorded as 4.85 s. What is thepercentage of error?

A 0.6 % B 2.1 %C 3.2 % D 5.2 %E 7.7 %

11 Which of the following statements

about errors is correct?

A Zero error is random errorB Random errors can be reducedby taking

repeat readings.C Systematic errors can be dueto

instruments which are notsensitive.D Systematic errors cause the

readings scattered on both

sides of the actual value.

12 Which of the following experimenttechniques can reduce systematicerror of the quantity beingmeasured?

A Measuring the diameter of awire at different points alongthe wire.

B Adjusting an ammeter to readzero before measuring acurrent.

C Timing a large number of oscillations to find the periodof a pendulum.

D Measuring the thickness of alarge number of pieces of paper to find the thickness of one piece.

13 The error is caused by theposition of eye is not parallel tothe scale of an instrument is calledas

A positive zero errorB negative zero errorC parallax error

14 The following table shows thereadings measured by usingdifferent measuring instruments X,

Y dan Z.Measuringinstrument

Reading /mm

X YZ

2.38526.5

Which of the following is true?X Y Z

A Ruler Vernier calipersMikrometer

screw gaugeB Vernier Mikrometer

Measuringcalipers screw gauge

tapeC Measuring Ruler

Vernier Tape

calipersD Mikrometer Ruler

VernierScrew gauge

Calipers

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15 Table shows readings of thethickness of a book measured byfour different students. Which of the students recorded the truereadings.

Student

Ruler/ cm

Verniercalipers/ cm

Mikrometerscrewgauge/cm

ABCD

WX

YZ

2.172.1742.172.2

2.22.22.1742.17

2.1742.172.22.174

16 Which of the following accuracy of

the measuring instruments is true?

Measuring instrumentsAccuracy

A Ruler 1 mmB Vernier calipers0.001 cmC Mikrometer screw gauge 0.1mm

17 The focal length of a convex lensis 12 cm. If the focal length ismeasured by using a ruler, thereading recorded ought to be

A 11.9 cm B 12.0cm

C 12.00 cm D 12.1cm

18 The diagram shows the existenceof zero errors of a vernier calipers.

What is the value of the zeroerror?

A + 0.04 cm B - 0.04 cmC + 0.06 cm D - 0.06 cm

19 The following diagram shows avernier calipers.

What is the reading of the verniercalipers ?

A 3.17 cm B 3.08cm

C 2.18 cm C 2.07cm

20 Figure(a) shows the existence of zero error of a vernier calipers.Figure(b) shows the reading of thevernier calipers for diameter of metal sphere.

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The actual reading of diameter of the metal sphere is

A 2.02 cm B 2.04cm

C 2.06 cm D 2.08cm

21 The thickness of a paper ismeasured by using a micrometer

screw gauge should be recordedas

A 2 mm B 2.1 mmC 2.14 mm D 2.142

mm22 Diagram shows a micrometerscrew gauge.

Based on the diagram, what is thenumber of revolution of thethimble.A 12 B 12½C 13 D 13¾

23 Diagram shows a micrometerscrew gauge reading when it isclosed at its gap.

The subsequent readings must be

corrected byA adding 0.02 mmB subtracting 0.02 mmC adding 0.03 mmD subtracting 0.03 mm

24

Based on the diagram above, thethickness of a sheet of paper is

A 3.25 cm B 3.75cm

C 0.325 cm D 0.0375cm

25 Figure(a) shows the existence of zero error of a micrometer screwgauge. Figure(b) shows thereading of the micrometer screwgauge for diameter of metal wire.

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The actual reading of diameter of the metal wire is

A 8.30 mm B 8.32 mmC 8.80 mm D 8.82 mm

26 A simple pendulum makes 20complete swings in 20.35 s.Which of the following is used?

A Stop watchB Pendulum clockC Electronic watch

27 A mass hanging from one end of avertical spring makes tencomplete oscillations in 15 s.

If the time of the oscillations istaken by a stop watch ,it shouldbe recorded as

A 15 s B 15.0 sC 15.00 s D 15.000 s

28 The figure shows a thermometer.

What is the reading shown?

A 96o C B 93.5o C

C 94.0 o C D 94o C

29 Which of the following will increasethe sensitivity of a mercury-in-glass thermometer/

Glassstemwall

Capillary tube

Size of bore

A thick wide bigB thin narrow bigC thick wide smallD thin narrow small

30 The current flows through a metalconductor is between 0.01 A to0.05 A. Which ammeter is mostsuitable to use?

A Ammeter range 0-1AB Ammeter range 0-5AC Ammeter range 0-10 mA

D Ammeter range 0-50 mA

31 What is the reading shown by theammeter above?

A 2.4 A B 2.80 A

C 0.48 A D 0.44 A

32 The function of zero adjuster in anammeter is to

A avoid zero errorB fasten the pointerC avoid parallax errorD control the very large current

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33

Measurement

Measuring

Instrument

Accuracy(cm)

Diameterof acopperwireLength of a pencilInternaldiameterof abeaker

(a) Complete the table above.(b) State one reason why thediameter of the

copper wire should bemeasured at a few

different places?

…………………………………………………

…………………………………………………(c) State one precaution to betaken while

taking measurements by usingthe

instrument which measuredthe internal diameter of abeaker.

………………………………………

…………

…………………………………………………

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Figure(a) shows the jaws of avernier calipers without tigh anyobject. Figure(b) shows the jaws of the vernier calipers tigh a testtube.

(a) What is the function of P?

.............................................................................

(b) What is the smallest divisionon the vernier scale?

.............................................................................

(c) State the diameter of the testtube in metre.

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35

Diagram above shows the readingof a mikrometer screw gauge forthe thickness of 5 sheets of paper.

(a) What is the number of revolution of the N scale .

(b) Determine the thickness of asheet of the paper in cm.

(c) Give the name and thefunction of M scale.

....................................................................

....................................................................

....................................................................

(d) State a precaution to betaken while takingmeasurements by using themicrometer screw gauge.

....................................................................

....................................................................36

Diagram above shows a

thermometer.

(a) Name component

(i) P……………………………...........

(ii) Q……………………………...........

(b) State the accuracy of thethermometer.

....................................................................(c) What is the reading of the

thermometer?

....................................................................

(d) Why does the glass stem wallof the thermometer is thin?

.................................................

...................(e) How should you do to increase

the accuracy of thethermometer.

....................................................................

…………………………………………………(f) Why does the thermometer

use mercury?

.................................................

...................

.................................................

...................

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(g) Draw a dotted line to show

the correct position of eye in

the above diagram whilemeasuring the temperature of a substance.

37 Diagram shows a miliammeter.(a) Give the name and the

function of component of

(i) A...........................................

……..................

....................................................................

(ii) B

……………………………………..................

....................................................................(b) State the accuracy of the

ammeter

....................................................................

....................................................................

(c) State the reading of theammeter.

....................................................................

....................................................................

(d) State two precautions to betaken while takingmeasurements by using theammeter..................................................

...................

…………………………………………………

…………………………………………………

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Lesson 3 - Understanding Measurements