1.4 Understanding Measurements

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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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1.4 Understanding Measurements

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