chapter 02 measurement

8/2/2019 Chapter 02 Measurement

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The unique value of science is its ability to make predictions. Scientific predictions arepossible because science only deals with physical quantities that can be measured.

2Chapter

Measurement


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2.1 Measurement of

Length

Chapter 2: Measurement


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1. Rulers and Measuring Tapes

2. Vernier Calipers 3. Micrometer ScrewGauge

Length & Measurement



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For accurate length measurement using a ruler, the

eye should be positioned in line and perpendicular tothe point to be read in order to avoid parallax error.

Parallax error

Parallax errors can also be reducedwhen measuring irregular shapeobject by using set-squares.



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Metre Rule and Measuring Tape

The metre rule is used to measure lengths up to 1.00 m.

Both the metre rule and measuring tape has aprecision of 1 mm.

If the ends of a metre rule are worn out

The length of the object is thedifference between the readings ofits end points.

Use of Metre Rule



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For very small length measurements, like the diameter of athin wire, a ruler is unable to yield accurate results.

Instruments such as vernier calipers and micrometer screwgauges are used.

Hence,

Vernier Calipers

Micrometer Screw Gauge



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Vernier Calipers

Vernier calipers make use of a main scale and a vernier

scale to increase its precision to 0.1 mm.

The range of a set of vernier calipers is typically around10 to 15 cm.

The following picture shows the components of a vernier caliper:



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Main scale

Vernier scale

2.1? cm

0.04 cm

2.14 cm

Vernier calipers can measure small lengths

accurately up to 2 decimal places in cm.

How to read

1. Write down main scale reading

2. Add vernier scale reading

Using Vernier Calipers



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Due to wear and tear, vernier calipers may not give zero

reading when the jaws are fully closed.

Vernier Calipers

This results in

and this must beaccounted for incalculations

For example,If the reading on a vernier scale = 3.22 cmZero error = - 0.07 cmDiameter of cylinder = 3.22 + 0.07 = 3.29 cm



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Micrometer Screw Gauge

The micrometer screw gauge makes use of a main scale and a

thimble scale to improve its precision to 0.01 mm.The range of a micrometer screw gauge is around 2.5 cm.

The main scale is marked indivisions of 0.5 mm.

The thimble scale has 50 divisions.

Each division measures 0.01 mm.



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How to read

1. Write down main scale (sleeve) reading

2. Add thimble scale reading

Sleeve scale

Thimble scale

4.5? mm

0.12 mm

4.62 mm

A micrometer screw gauge can measure small

lengths accurately up to 2 decimal places in mm.

Using Micrometer Screw Gauge



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Measurement of Time

Stopwatches, are the most common instrument for

measuring time in the school laboratory. SI unit for time issecond.

The uncertainty introduced by the random reaction of aperson is known as human reaction time error. It is typicallyof the order of 0.1 to 0.2 s.



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2.2 Scales



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Linear and Non-Linear Scales

A linear scale is one inwhich the divisions ofthe units are equallyspaced.

A non-linear scale isone in which thedivisions of the units arenot equally spaced.



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Digital and Analogue Scales

The readings for a digital meterchanges by a fixed minimumamount and can be read-offdirectly from the display.

The reading of an analoguescale is estimated from anindicator that movesover a scale.



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2.3 Errors



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Measurement errors are the uncertainties in a measurement due to thelimitations of the instruments or methods used for the measurement.

Note that,True value = Measured value Experimental error

When recording a measurement, it is important to record the

uncertainty of the measurement as well.

Two concepts that are related to errors are:

1. Accuracy

2 . Precision



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Accuracy

Accuracy is the closeness of a measurement of a physical

quantity to the true value.



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Precision

Precision refers to the closeness of several measurements.

If repeated measurements of a quantity are very close toeach other, we say that the measurements are precise.



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Combining errors or uncertainties

We often encounter physical quantities that are the sum or productsof different measurements. In such cases, the calculated error oruncertainty is combined using a few simple rules:

1. Addition and subtractionWhen adding two or more quantities, the total uncertainty is

given by the sum of the uncertainty of the individual quantity.

2. Multiplication and divisionWhen multiplying or dividing two or more quantities, the totalfractional uncertainty is given by the sum of the fractional

uncertainty of the individual quantity.



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2.4 Simple Pendulum



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Galileo investigated the characteristics of a pendulums motion

and discovered that its period:

is independent of the bobs mass; is independent of its amplitude; and varies directly with the square-root

of its length.

The period of a pendulum is the time taken for the bob to moveone complete oscillation

The amplitude of the oscillation is the maximum displacement ofthe pendulum bob.



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2.5 Area



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Area is a quantity that measures the size of a surface.The SI unit for area is square metres, m2.

The area of a square of length, l= ll= l2

The area of a rectangle = length breadth = lb

The area of a circle of radius r= r2

The area of a triangle = 1/2 (base height)

The area of a trapezium = 1/2 (sum of parallel sides) height



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2.6 Volume



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2.7 Density



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5 kg

8 kg


Why did the 5-kgcylinder sink instead

of the 8-kg prism?


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Lets take a look at the two boxes, A and B. Compare box A and box B.

Similarity:

Difference:

Density =Mass

Volume

Volume

Defining density

Density is defined as mass per unit volume . It is a derived quantity.

We say that box A has a higher density than box B.

SI unit of density is kg/m3.

Mass

kg

m3 1 g/cm3 = 1 000 kg/m3



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Relative Density

Relative density (RD) is the ratio of the density of a given

substance to the density of a reference substance. Relativedensity does not have a unit as it is a ratio.

RD = Density of substanceDensity of reference substance

chapter 02 measurement

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