1.4measurement-Edit u Handout

7/31/2019 1.4measurement-Edit u Handout

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Nature of measurement

Measurements are trials to determine the true value of aparticular physical quantity

The difference between the true value of a quantity and

the value obtained in measurement is the error

To measure is to make an acceptable estimate.A suitable instrument must be used

An estimate of the value of a quantity is made beforedeciding on the right measuring instrument to be used.


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It is very important to choose an appropriateinstrument for measuring a physical quantity

We need to consider its magnitude and thenchoose a suitable instrument

The magnitude of the quantity should notexceed the max capacity of the instrument

The instrument must be sensitive enough todetect and give a meaningful measurement ofthe quantity

Eg:(i) metre rule length of a book

(ii) measuring tape length of a table


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Measuring instruments

Internal jaw : measuring inner dimensions

External jaw : measuring outer dimensions Stem : measuring depths

(a) Vernier callipers


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Vernier calliper

To measure lengths of less than 10 cm

Suitable to measure internal and externaldiameter of round objects

Its accuracy is up to 0.01 cm Has two scale:

(i) main scale : made up of 10 equal parts

(ii) vernier scale : 10 parts are equal to

0.9 cm=9mm


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How to read??Reading of MS= 2.1 cm

Reading of VS = 0.05 cm

The reading of verniercalliper,X

= MS + VS

= 2.15 cm

STEP 1STEP 2


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Step 1:

Read off the main scale where the zero ofthe vernier scale is

- Reading of main scale= 2.1 cm

Step 2

-read off the vernier scale where the vernier

scale line aligned with the main scale line- Reading of vernier scale = 0.05 cm


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Reading of MS= 2.1 cm

Reading of VS = 0.05 cm

The reading of vernier calliper,X = MS + VS

= 2.15 cm


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Zero error need to be determined (without object) beforeusing the vernier calliper

(a) no zero error

(b) zero error

(i) positive zero error (ii) negative zero error

Zero error = + 0.07 cm Zero error = - 0.07 cm


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The reading should be corrected if there is zero error

Actual reading = measured reading zero error


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Positive zero error Negative zero error

Withoutobject

Zero error= Zero error=

With object

Main scale=

Vernier scale=

Reading=

Main scale=

Vernier scale=

Reading=

Actual reading Actual reading

=

=

=

=


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(b) Micrometer screw gauge

To measure very small object (thickness of a coin, diameter of cooper wire)

Accuracy is up to 0.01 mm

The presision is higher than vernier calliper

Have two part of scale

(i) main scale (on the sleeve)

(ii) vernier scale (on the thimble)


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Main scale consists of horizontal line in the centre (centre line) and

two series of scale line respectively above and below that centre line

The distance between two consecutive scale above or below the

centre line is 1 mm

the distance between the consecutive scale lineand the lower scale line is 0.5mm

The vernier scale consists of 50 small divisions

One part of the vernier scale is 0.01mm


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How to read?

STEP 1

STEP 2


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STEP 1

Read off the main scale where the edge of thethimble is, that is 7.5 mm

STEP 2

Read off the vernier scale where the line on thevernier scale is aligned with the centre line of themain scale

The line 22nd line on the vernier scale is alignedwith the centre line of the main scale, that is, 22 x0.01mm= 0.22 mm


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Reading of MS= 7.5 mm

Reading of VS = 0.22 mm

Reading of micrometer = MS + VS

= 7.5 mm + 0.22mm

= 7.72mm


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Zero error need to be determined (without object) beforeusing the micrometer screw gauge

(a) no zero error

(b) zero error

(i) positive zero error (ii) negative zero error

Zero error = + 0.01mm Zero error = - 0.02mm

P i i N i


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Positive zero error Negative zero error

Withoutobject

Zero error= Zero error=

With

object

MS =VS =

Reading =

MS =VS =

Reading =

Actual reading Actual reading==

=

=

=


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PRECISION, ACCURACY AND SENSITIVITY

Uncertainties could occur in a measurement due to

(i) inaccuracy of the measuring instrument

(ii) a mistake in the measuring process

(iii) a mistake in the scale reading of a measuringinstrument

The measured value can closely approximate the actualvalue if we use measuring instruments which have highprecision and accuracy


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PRECISION

Is the ability of the instrument to measure a quantity in aconsistent manner with little or no deviation amongmeasurements

Relative deviation is the percentage of mean deviation for a

set of measurement.

100%mean value

devitionmeandeviationrelative


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Example 1

Experiment number 1 2 3

Reading for the rod length(cm) 27.0 26.0 25.5The table shows the result for the measurement of a specific lengthof rod. Calculate the relative deviation for this experiment.

Solution:

Mean rod length = (27 + 26.0 + 25.5) 3 = 26.2 cm

Mean deviation = (0.8 + 0.2 + 0.7) 3 = 0.567 cm

Relative deviation = (0.567 26.2) x 100% = 2.16%

Reading Deviation

27.0 27.0 26.2 = 0.8

26.0 26.0 26.2 = 0.225.5 25.5 26.2 = 0.7


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ACCURACY

Is the approximation of the measurement to the actual

value for a certain quantity of physics. The measurement is more accurate if its number of

significant figures increases

The diagram shows that the micrometer screw gauge is moreaccurate than the other measuring instrument

Measuring instrument used

for measuring

Thickness of a book

(cm)Metre rule

Vernier Caliper

Micrometer screw gauge

5.2

5.22

5.223


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The accuracy of measurement can be increasedby

(i) taking a number of repeat readings to

calculate the mean value of the reading(ii) avoiding the end error or zero errors

(iii) taking into account the zero and parallax

errors(iv) using more sensitive equipment such as avernier caliper to replace a ruler


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Accurate and precise

Precise but less accurate

Not accurate and not

precise

Different between precision and accuracy

Accurate but less precise

1

2

3

4


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Sensitivity

Is the ability to detect small changes in the quantity that isbeing measured

Measuring instruments that have smaller scale parts are moresensitive

Sensitive instrument need not necessarily accurate

Between vernier caliper and metre rule whenmeasuring the thickness of a piece of wire, avernier caliper is more sensitive than a metre rule


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Error in measurement

No measurement is exact. All measurements willhave some degree of error or uncertainty

There are two main types of errors:

(i) systematic errors

(ii) random error


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Systematic error Is the error of a measurement which causes the measuring

quantity to differ from the actual value

Originates from the measuring instrument itself

Causes all readings that have been obtained to be alwaysbigger or smaller than the actual value

Example:

(i) zero error- is error of obtaining a certain reading (measurement)

when in actuality the measuring instrument should give azero reading

- zero error on ammeter can be avoided by turning the zero

adjuster so that the pointer is exactly on the zero mark(ii) end error

Can be reduce by

(i) conducting the experiment with care

(ii) repeating the experiment by using different instrument

R d


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Random error is reading error caused by an incorrect eye position of

the observer as per the scale mark while the

measurement is been taken Also occur when is a sudden a change of environmental

factor temperature, air circulation or lighting

Can be reduced by

(i) taking repeat readings

(ii) measuring the average value of the reading

X

X Correct reading= 1.6 cm

Error in reading = 1.7 cm

Error in reading = 1.5 cm

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