Lesson_3_-_Understanding_measurements[1]

8/7/2019 Lesson_3_-_Understanding_measurements[1]

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Introduction

The characteristics which are emphasized in theselection of a measuring instrument includeprecision , accuracy and sensitivity.

The meaning of Precision, Accuracy andSensitivity.

Precision is the degree of uniformity orreproducibility of the measurements.OR

Precision is the degree of a measuringinstrument to record consistent reading foreach measurement by the same way.

When we say the measurements are consistent,we mean that all the values of the measurementsare close together.

Accuracy is the degree of closeness of themeasurements to the actual or accepted value.

When we say the measurements are accurate,

we are actually saying that the values of themeasurements are close to the true oraccepted value.The diagram shows the result for four shootersA, B , C and D in a tournament. Every shootersshot five times .

The table shows the conclusion .

Shooter Precision AccuracyA High Low

B Low High

C High HighD Low Low

Sensitivity of a measuring instrument is definedas the capability of that instrument to respond tophysical stimuli or to register small physicalamount or differences.ORSensitivity is the degree of a measuringinstrument to record small change in its reading.

The smallest scale division on the measuringinstruments shows the sensitivity of theinstruments. Thus the more sensitive themeasuring instruments the finer the scale

divisions.

A vernier calipers is more sensitive than a ruler ora miliammeter is more sensitive than an ammeter.A sensitive instrument is not always an accurateinstrument.

Errors

Any measurement of a physical quantity haserrors or uncertainty.There are two types of errors.

(a) Systematic errors(b) Random errorsSystematic errorsSystematic errors are errors in the measurementof a physical quantity due to instruments, theeffects of surrounding conditions and physicalconstraints of the observer.The main characteristic of systematic error is thatits magnitude is almost constant or appears inone direction only. The value of the measurementis always greater or is always less than the actual

value.

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

Zero errors occurs when the instrumentgives a non- zero reading when in fact theactual reading is zero.

(ii) Personal error of the observer.

LESSON 3Precision(consistency )andAccuracy ,Sensitivity and Error


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Physical constraints or limitations of theobserver can cause systematic errors.An example is the reaction time.

(iii) Errors due to instrumentsThe examples are;A stopwatch which is faster than normal

would give readings which are always largerthan the actual time.A thermometer which is used under differentconditions from which it was calibrated.A voltmeter manufactured in Germany hadbeen calibarated under different temperatureand earths magnetic field from Malaysiawhere the voltmeter is used.

(iv) Errors due to wrong assumption.For example, we assumed that the value ofthe acceleration due to gravity g is 9.81 ms-2,but the actual value may 9.79 ms-2. Hence

there is a positive error of 0.02 ms -2.

Systematic errors cannot be reduced oreliminated by taking repeated readings using thesame method, the same instrument or by thesame observer.Systematic erros can be elimated or reduced byimproving the procedure of taking themeasurements , using a different instrument orgetting somebody else to make the themeasurements.For example for the zero errors can be eliminated

by subtracting the zero reading from the obtainedreadings.

Random errors

The main source of random error is the observeror has non -constant size of error and isunpredictable.The characteristics of random errors are:

(i) it can be positive or negative. Theobtained readings may be greater orless than the actual value.

(ii) its magnitude is not constant.Examples of random errors are:(i) Parallax errors occur when the

position of the eye is not perpendicularto the scale.

(ii) Different pressures are applied whenclosing the gap of the micrometerscrew gauge when it is used to measurethe diameter of a wire.

(iii) Changes in the temperature during anexperiment.

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

To eliminate or reduce random errors , repeatedreading are taken.

Measurement Length

We normally use ruler, measuring tape , verniercalipers or micrometer screw gauge to measurelength.

Measuringinstrument

Smallest scaledivision

Ruler 0.1 cm or1 mm

Verniercalipers

0.01cm

Micrometerscrew gauge

0.01 mm

Vernier calipers

A pair of vernier calipers can be used to measurethickness of a wire , internal and externaldiameter of a beaker, depths of a test tube ,etc.The inside jaws are used to measure internaldiameters and the outside jaws are used tomeasure external diameters and thickness.The tail is used to measure depths.The main scale is marked in divisions of 0.1 cm ,while the vernier scale is marked in divisions of0.01 cm.

The following steps shows how to read thevernier calipers.

y Read the main scale marking just beforethe zero marking on the vernier scale.

y Find the vernier scale marking whichjoins the main scale marking.


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y The reading for a vernier scale is alwaysrecorded in cm with two decimal places(The accuracy is 0.01 cm)

Example 1

Write down the reading of the following verniercalipers.

Solution

Example 2

Based on the following diagrams write down theactual thickness of the objects.

Solution

Micrometer screw gauge

The micrometer screw gauge is used to measurethickness and diameters of very small objects.The main scale is marked in divisions of 0.5 mm ,while the vernier scale is marked in divisions of0.01 mm.

The jaws tight the object that is to be measured.The thimble is turned until its jaw touches theobject.The ratchet knob prevents over tightening bymaking a click sound when the micrometer isready to be read.

The following steps shows how to read the

micrometer screw gauge.Read the main scale marking just before the zeromarking on the vernier scale.

y Read the main scale marking just beforethe zero marking beforev the thimble.

y Find the vernier scale marking whichjoins the main scale.

y The reading for a micrometer screwgauge is always recorded in mm with twodecimal places(The accuracy is 0.01 cm)

Example 3Write down the reading of the following diagrams.


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Solution

Example 4Based on the following diagrams write down theactual diameters of the objects(a)

(b)

Solution

Measurement Mass

Accuracy : ..Reading : .

Accuracy : ..Reading : .


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Triple beam balance

Accuracy : .

Measurement Time

Mechanical stop watch

Accuracy : ..

Electronic stop watch

Accuracy :Reading :.Measurement Current

Ammeter range 0 5AAccuracy :.

Double-scale ammeter

Accuracy of upper scale :..Accuracy of lower scale : .

Reading :..

Miliammeter range 0- 50 mA

Accuracy:

Reading :..

Measurement Temperature


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Accuracy:..

1 The ability of an instrument gives consistentreading , when repeated readings are taken

is called as

A accuracy B precisionC sensitivity D error

2 Which of the following should be the smallvalue ,so that the precision becomes high?

A Actual value B MeanC Relative error D Relative

deviation

3 The ability of an instrument to detect aslight change that occurs in the measuredquantity is called as

A precision B accuracyC sensitivity D error

4 The accuracy of an instrument increases if

A the number of significant figuresincreases

B the relative deviation relative increasesC the relative error increases

5 Based on the table below, what are themeasuring instruments J, K and L?

Measuring instruments MeasurementJ 2.52

0.01 cm

K 15.2

0.1 cm

L 125.4

0.1 g

J K LA Micrometer Vernier Spring

screw gauge calipers balanceB Micrometer Vernier Triple beam

Screw gauge calipers balance

C Vernier Metre Triple beamcalipers ruler balance

6 Which of the following is true?

A The parallax error is not effected to the

accuracyB The accurate instrument is also the

sensitive instrumentC The accuracy increases when the

measurement nearest to actual value.

7 Which of the following is true?

A A stop watch is more sensitive than anelectronic

B An ammeter is more sensitive than agalvanometer

C A vernier calipers is more sensitivethan a micrometer screw gauge

D A thinner-walled bulb thermometer ismore sensitive than a thicker

walledbulb thermometer

8 Which of the following is most likely toshow a precise shooting?

9 Which of the following is most likely to showan accurate shooting but not so presicely?

TUTORIAL 3


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10 It take 5.01 s for an object to move to acertain distance. When an electronic watch isused the time is recorded as 4.85 s. What isthe percentage of error?

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

11 Which of the following statements abouterrors is correct?

A Zero error is random errorB Random errors can be reduced bytaking

repeat readings.C Systematic errors can be due to

instruments which are not sensitive.D Systematic errors cause the readings

scattered on both sides of the actualvalue.

12 Which of the following experiment

techniques can reduce systematic error ofthe quantity being measured?

A Measuring the diameter of a wire atdifferent points along the wire.

B Adjusting an ammeter to read zerobefore measuring a current.

C Timing a large number of oscillations tofind the period of a pendulum.

D Measuring the thickness of a largenumber of pieces of paper to find thethickness of one piece.

13 The error is caused by the position of eye isnot parallel to the scale of an instrument iscalled as

A positive zero errorB negative zero errorC parallax error

14 The following table shows the readingsmeasured by using different measuringinstruments X, Y and Z.

Measuringinstrument

Reading /mm

X

YZ

2.38

526.5

Which of the following is true?X Y Z

A Ruler Vernier calipers Micrometerscrew gauge

B Vernier Micrometer Measuringcalipers screw gauge tape

C Measuring Ruler VernierTape calipers

D Micrometer Ruler VernierScrew gauge Calipers

15 Table shows readings of the thickness of abook measured by four different students.Which of the students recorded the truereadings.

Student Ruler/ cm

Verniercalipers/ cm

Micrometerscrewgauge/cm

A

BCD

W

XYZ

2.17

2.1742.172.2

2.2

2.22.1742.17

2.174

2.172.22.174

16 Which of the following accuracy of themeasuring instruments is true?

Measuring instruments Accuracy

A Ruler 1 mmB Vernier calipers 0.001 cmC Micrometer screw gauge 0.1 mm

17 The focal length of a convex lens is 12 cm. Ifthe focal length is measured by using a ruler,the reading recorded ought to be

A 11.9 cm B 12.0 cmC 12.00 cm D 12.1 cm


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18 The diagram shows the existence of zeroerrors of a vernier calipers.

What is the value of the zero error?

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

19 The following diagram shows a verniercalipers.

What is the reading of the vernier calipers ?

A 3.17 cm B 3.08 cmC 2.18 cm C 2.07 cm

20 Figure(a) shows the existence of zero errorof a vernier calipers. Figure(b) shows thereading of the vernier calipers for diameter

of metal sphere.

The actual reading of diameter of the metalsphere is

A 2.02 cm B 2.04 cmC 2.06 cm D 2.08 cm

21 The thickness of a paper is measured byusing a micrometer screw gauge should berecorded as

A 2 mm B 2.1 mmC 2.14 mm D 2.142 mm

22 Diagram shows a micrometer screw gauge.

Based on the diagram ,what is the number ofrevolution of the timble.A 12 B 12C 13 D 13


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23 Diagram shows a micrometer screw gaugereading when it is closed at its gap.

The subsequent readings must be correctedby

A adding 0.02 mmB subtracting 0.02 mmC adding 0.03 mmD subtracting 0.03 mm

24

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

A 3.25 cm B 3.75 cmC 0.325 cm D 0.0375 cm

25 Figure(a) shows the existence of zero errorof a micrometer screw gauge. Figure(b)shows the reading of the micrometer screwgauge for diameter of metal wire.

The actual reading of diameter of the metalwire is

A 8.30 mm B 8.32 mmC 8.80 mm D 8.82 mm

26 A simple pendulum makes 20 completeswings in 20.35 s. Which of the following isused?

A Stop watchB Pendulum clockC Electronic watch

27 A mass hanging from one end of a verticalspring makes ten complete oscillations in 15s.If the time of the oscillations is taken by a

stop watch ,it should be 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 94.0o C D 94o C

29 Which of the following will increase thesensitivity of a mercury-in-glassthermometer?

Glassstem wall

Capillarytube

Size ofbore

A thick wide bigB thin narrow big

C thick wide smallD thin narrow small

30 The current flows through a metal conductoris between 0.01 A to 0.05 A. Whichammeter is most suitable to use?

A Ammeter range 0-1AB Ammeter range 0-5A


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C Ammeter range 0-10 mAD Ammeter range 0-50 mA

31 What is the reading shown by the ammeterabove?

A 2.4 A B 2.80 AC 0.48 A D 0.44 A

32 The function of zero adjuster in an ammeteris to

A avoid zero error

B fasten the pointerC avoid parallax errorD control the very large current

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Measurement

MeasuringInstrument

Accuracy(cm)

Diameter ofa copper

wireLength of apencil

Internaldiameter ofa beaker

(a) Complete the table above.

(b) State one reason why the diameter ofthe

copper wire should be measured at afew

different places?

(c) State one precaution to be taken while

taking measurements by using theinstrument which measured the internaldiameter of a beaker.

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Figure(a) shows the jaws of a verniercalipers without tigh any object. Figure(b)

shows the jaws of the vernier calipers tigh atest tube.

(a) What is the function of P?

...................................................................(b) What is the smallest division on the

vernier scale?


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....................................................................(c) State the diameter of the test tube in

metre.

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Diagram above shows the reading of amicrometer screw gauge for the thickness of5 sheets of paper.

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

(b) Determine the thickness of a sheet ofthe paper in cm.

(c) Give the name and the function of Mscale.

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

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

....................................................................(d) State a precaution to be taken while

taking measurements by using themicrometer screw gauge.

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

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Diagram above shows a thermometer.

(a) Name component

(i) P ...........

(ii) Q ...........

(b) State the accuracy of the thermometer.

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

thermometer?

....................................................................(d) Why does the glass stem wall of the

thermometer is thin?

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

(e) How should you do to increase theaccuracy of the thermometer.

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

(f) Why does the thermometer use

mercury?

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

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

(g) Draw a dotted line to show the correctposition of eye in the above diagramwhile measuring the temperature of asubstance.


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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 the ammeter.

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

....................................................................(d) State two precautions to be taken while

taking measurements by using theammeter.....................................................................

Lesson_3_-_Understanding_measurements[1]

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