Upload
maznin-mohamed
View
216
Download
0
Embed Size (px)
Citation preview
7/31/2019 1.4measurement-Edit u Handout
1/27
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.
7/31/2019 1.4measurement-Edit u Handout
2/27
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
7/31/2019 1.4measurement-Edit u Handout
3/27
Measuring instruments
Internal jaw : measuring inner dimensions
External jaw : measuring outer dimensions Stem : measuring depths
(a) Vernier callipers
7/31/2019 1.4measurement-Edit u Handout
4/27
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
7/31/2019 1.4measurement-Edit u Handout
5/27
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
7/31/2019 1.4measurement-Edit u Handout
6/27
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
7/31/2019 1.4measurement-Edit u Handout
7/27
Reading of MS= 2.1 cm
Reading of VS = 0.05 cm
The reading of vernier calliper,X = MS + VS
= 2.15 cm
7/31/2019 1.4measurement-Edit u Handout
8/27
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
7/31/2019 1.4measurement-Edit u Handout
9/27
The reading should be corrected if there is zero error
Actual reading = measured reading zero error
7/31/2019 1.4measurement-Edit u Handout
10/27
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
=
=
=
=
7/31/2019 1.4measurement-Edit u Handout
11/27
(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)
7/31/2019 1.4measurement-Edit u Handout
12/27
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
7/31/2019 1.4measurement-Edit u Handout
13/27
How to read?
STEP 1
STEP 2
7/31/2019 1.4measurement-Edit u Handout
14/27
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
7/31/2019 1.4measurement-Edit u Handout
15/27
Reading of MS= 7.5 mm
Reading of VS = 0.22 mm
Reading of micrometer = MS + VS
= 7.5 mm + 0.22mm
= 7.72mm
7/31/2019 1.4measurement-Edit u Handout
16/27
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
7/31/2019 1.4measurement-Edit u Handout
17/27
Positive zero error Negative zero error
Withoutobject
Zero error= Zero error=
With
object
MS =VS =
Reading =
MS =VS =
Reading =
Actual reading Actual reading==
=
=
=
7/31/2019 1.4measurement-Edit u Handout
18/27
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
7/31/2019 1.4measurement-Edit u Handout
19/27
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
7/31/2019 1.4measurement-Edit u Handout
20/27
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
7/31/2019 1.4measurement-Edit u Handout
21/27
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
7/31/2019 1.4measurement-Edit u Handout
22/27
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
7/31/2019 1.4measurement-Edit u Handout
23/27
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
7/31/2019 1.4measurement-Edit u Handout
24/27
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
7/31/2019 1.4measurement-Edit u Handout
25/27
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
7/31/2019 1.4measurement-Edit u Handout
26/27
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
7/31/2019 1.4measurement-Edit u Handout
27/27
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