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INTRODUCTION TO PHYSICS
Measurements
Measurements are trials to determine the actual value of a particular physical quantity.
Practical work in physics requires measurement.
Suitable instruments are required for measurement and the readings obtained must be
presented in suitable units.Examples:
Object Measuring Tools
Temperature of
boiling water
Thermometer
Running Time
Stop watch
Electric current
Ammeter
Accuracy
1. Accuracy of a measurement is how close the value of a measurement to
the actualvalue.
2. The level of accuracy is related to the relative error.
3. Relative error =valueActual
Errorx 100 %
4. An error is a difference between the measured value and the actual value
or true value .
5. Accuracy can be improved by : -
(a) repeated readings are taken and the average value is calculated
(b) avoid parallax errors
(c) avoid zero errors(d) use measuring instruments with a higher accuracy.
For example, a vernier callipers is more accurate than a ruler .
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Consistency
1. Consistency /Precision is the degree of an instrument to record consistentreadings for each measurement by the same way or the ability to record
the same readings when a measurement is repeated.
2. A measurement is considered consistent will have asmallrelative
deviation or no deviation from the average value .
3.. A deviation is a difference between a measurementvalue and its
average value .
4. average deviation =takenvaluesofnumbers
devition
5. relative deviation =valueaverage
deviationaveragex 100 %
Example:
A student used vernier callipers to measure diameter of a glass rod. The tablebelow shows the readings.
Measurement Diameter rod (cm) Deviation
1 2.23
2 2.26
3 2.24
4 2.235 2.25
Average
Average deviation =
Relative deviation =
6. Consistency can be improved by
(a) eliminating parallax errors(b) exercising greater care and effort when taking readings.
(c) using an instrument which is not defective.
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7. Comparisons between consistency and accuracy
a) Consistent but not accurate b) Accurate but not consistent
c) Accurate and consistent d) Not accurate and not consistent.
Sensitivity
1. Sensitivity of an instrument is its ability to detect a small changein thequantity to be measured.
2. A measuring instrument that has a scale with a smaller divisions is moresensitive .
3. Measuring instruments.
Measuring
instrument
Smallest magnitude
of quantity (cm)
Sensitivity / Accuracy
Metre rule 0.1 0.1 cm (low)
Vernier callipers 0.01 0.01 cm (moderate)
Micrometre screw
gauge
0.001 0.001 cm (high)
Experimental Error
1. An error is a difference between the true value of a quantity and the value
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obtained in measurement .
2. There are two main types of errors :(a) systematic errors
(b) random errors
3. Systematic errors
- are cumulative errors that can be corrected, if the errors are known.
- result from(a) an incorrect position of the zero point, known as zero error.
* A zero error arises when the measuring instrument does not
start from exactly zero.
(b) an incorrect calibration of the measuring instrument.
- can be eliminated or corrected if the measuring instruments are
calibrated or adjusted frequently.
4. Random errors
- arise from unknown and unpredictable variations in condition, andwill produce a different error every time you repeat the experiment.
- may be due to:
(a) personal error ( human limitations of sight and touch )(b) lack of sensitivity ( instrument does not respond / indicate
insignificant or small change )
(c) natural errors ( wind , temperature, humidity, refraction,
magnetic field or gravity )(d) wrong technique ( applying excessive pressure when
turning a micrometer screw gauge )
- can be minimized by repeating the measurement several times andtaking the average (mean) of the reading .
5. Parallax error- An error in reading a measurement because an observers eye and the
pointer are not in a line perpendicular to the plane of the scale .
(We should place our eyes directlyperpendicularin front of thepointer or scale of an instrument when taking measurements )
.
1.4.5 Measurement of length
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Instrument Example
Measuring tape To measure a waist of a man.
Metre rule To measure the length of a table
Vernier callipers To measure thickness of text book
Micrometre screwgauge
To measure a diameter of a glassrod or wire
A. Metre rule
To measure length from a few cm up to 1 m.
1. Precautions to be taken when using a ruler:
(a) ensure that the object is in contact with the ruler to avoidinaccurate readings.
(b) avoid parallax errors
(c) avoid zero error and end error.
2. For example: A ruler is to determine the diameter of the wire.
Solution:
Length of wire
Diameter of wire, d = ----------------------------
No. of coils
1.5 - 1.0= -------------------
10
= 0.05 cm
B. Vernier callipers
1. Two pairs of jaws
(a) outside jaws: to measure linear dimensions and ______diameters
(b) inside jaws : to measure _____________ diameters
2. Two steel bar scales
(a) the main scale
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(b) the vernier scale - has a scale on which ten divisions are equal to
nine small divisions on the main scale .
3. Errors in the vernier callipers
(a) No zero error
(b) Positive zero error
Positive zero error = + 0.04 cm
(c) Negative zero error
Negative zero error = - ( 1.0 - 0.08 )
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= - 0.02 cm
4. For example: Figure below shows the use of a vernier callipers tomeasure the size of spherical object. Determine the correct size of
the object if the zero error of the vernier callipers is
(a) - 0.08 cm(b) + 0.08 cm
Example 1 :
(a) Zero error = - 0.08 cm
Main scale reading = 2.10 cm
Vernier scale reading = 0.05 cmVernier caliper reading = 2 . 1 + 0.05 = 2.15 cm
Correct size of object = vernier caliper reading - zero reading
= 2.15 - ( -0.08 ) = 2.23 cm
(b) Correct size of object = 2.15 - ( +0.08 ) = 2. 07 cm
Example 2 :
(a) Zero error = __________
Main scale reading = _____________
Vernier scale reading = _____________
Vernier callipers reading = ______________Correct size of object = vernier callipers reading - zero reading
= _____________= __________
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(b) Correct size of object = ____________ = __________
C. Micrometer Screw Gauge
1. Comprises of
(a) main scale on the sleeve(b) thimble scale on the thimble
2. Errors in micrometer screw gauge(a) No zero error
(b) Positive zero error
Zero error = + 0.04 mm
Correct reading = micrometer reading - ( +0.04 )
(c) Negative zero error
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Zero error = -0.003 mm
Correct reading = micrometer - ( -0.03 )
Figure below shows a micrometer screw gauge used to measure the sizeof an object.
Determine the size of the object if the micrometer has a zero error of
(a) + 0.01 mm(b) - 0.03 mm
Example 1 :
Solution :
The main scale reading = 4.50 mmThe thimble scale reading = 0.21 mm
The reading of the gauge = 4.50 + 0.21 = 4.71 mm
(a) Size of object = the reading of the gauge - zero error
= 4.71 - 0.01
= 4.70 mm
(b) Size of object = 4.71 - ( - 0.03 )= 4.74 mm
Example 2 :
Solution :
The main scale reading = ________The thimble scale reading = ________
The reading of the gauge = ________
(a) Size of object = the reading of the gauge - zero error
= ______________= _________
(b) Size of object = ________________
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= __________
1.4.6 Measurement of time1. Stop watches are used to measure time interval.
2. Two types of stop watches(a) The _____________stop watch which is mechanically operated
(b) The ____________stop watch which is electronically operated.
1.4.7 Measurement of massThe mass of an object can be measured using a beam balance or an
electronic balance.
1.4.8 Measurement of temperature
1. A thermometer is an instrument used to measure temperature.
2. Types of thermometer(a) clinical thermometer
(b) mercury thermometer (range 100C to 1100C with an
accuracy of 10C )(c) mercury thermometer (range 0 0C to 360 0C with an accuracy
of 2 0C )
3. A mercury thermometer is a sensitive instrument because:
(a) Mercury is a liquid metal which is sensitive to temperature
changes. It expands and contracts uniformly with thetemperature.
(b) The thin walled glass bulb allows a quick heat transfer
between the heat source and the mercury.(c) The capillary tube, which has a small diameter, amplifies a
small expansion in the bulb into a large linear expansion along
the length of the capillary tube.
1.4.9 Measurement of electric current and voltage
A. Ammeter1. An instrument used to measure the amount of _____________
____________ flowing through a particular point in an
electrical circuit.2. The SI unit for current is____________, A
3. For a small current, a milliammeter is used.
( an accuracy of 0.1 mA or 0.2 mA is used )
4. It is usually connected in series in an electrical circuit .
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B. Voltmeter1. An instrument used to measure the potential difference
(__________) between any two points in an electrical circuit.
2. The SI unit for potential difference is__________, V.
3. It is connected in parallel in an electrical circuit.
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