1Physics&Measurement

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Physics in Context

SC3105

By

Cik Roshidah bt Mat


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Physics and measurement

in everyday life

Introduction

Conversion of units

Scientific notation

Accuracy and precision

Significant digits

Techniques of good measurement


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1.1 Physical Quantities and UnitsPhysical quantity: Any number that is used to describe a physical

phenomenon quantitatively

Consists of:

Basic quantities Derived Quantities


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1.1 Physical Quantities and Units

International System, SIUnit:

The most common unit used by scientists andengineers around the world


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Basic quantities S Units

Length meter [m] Time second [s] Mass kilogram [kg] Current ampere [A] Temperature kelvin [K] Amount of Substance mole [n] (Light Intensity) candela [cd]

Quantities SIUnits Symbols


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1.1 Physical Quantities and Units

Derived Quantities:

Combinations of the basic quantities Units for derived quantities can be deduced if

the definitions are given


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Determining the Derived Units:Example:

Define the quantity:

Density ()is the mass (m) of an object per unit volume (V)

Hence the defining equation in SI units

= m / V (kg / m3) This gives the derived SI unit for density as kilograms per cubic meter. (kg / m3)

Try this: What are the units of ?

(Clue : The relationship between the circumference (c) and the diameter (d) of a

circle is given by the equation c= d

If length is measured in meters, then= c /d (m / m)

Thus the constant has no units, because they cancel out. It is unitlessordimensionless constant.


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Unit Prefixes

Tera T 1012

Giga G 109

Mega M 106

Kilo k 103

Hecto h 102

Deka da 101

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro 10-6

Nano n 10-9

Pico p 10-12

Femto f 10-15

Prefix Symbol Factor


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Unit Consistency and Conversions Equation must always be dimensionally

consistent

example: d= 10m, v = 2ms-1 and t = 5s

d = vt

10 2 5m

m s

s

in terms of unit:


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Conversion of Unit

When converting between units, write down the

units explicitly in the calculations and treat themlike any algebraic quantity.

In particular, take advantage of the fact that

multiplying or dividing an equation by a factorof 1 does not alter and equation.


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Conversion of Unit Example:

Express 979.0 m in feet.

(3.281 feet = 1 meter)

Solution:

Use (3.281 feet / 1 meter) as a conversion factor to multiply theequation Length = 979.0 meters

Length = (979.0 m)(1)= (979.0 meters) (3.281 feet / 1 meter)

= 3212 feet


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Significant Figures

Measured quantities contain uncertainty

Only retain figures that contain meaningfulinformation


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Significant Figures Significant figures(sometimes called significant digits) is

all non-zero digits plus zeros that do not just hold a place before or aftera decimal point.

used to indicate the number of meaningful digits

The number of s.f. of a numerical quantity is the number ofreliably known digits it contains.

example: 2.91mm (3s.f.)

For a measured quantity, s.f. is usually defined as all of the digitsthat can be read directly from the instrument used in making themeasurement plus one uncertain digit that is obtained byestimating the fraction of the smallest division of theinstruments scale.


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Significant Figures Zeros at the beginning of a number are not significant.

They merely locate the decimal point. e.g. 0.0254 (3 s.f. - 2,5,4)

Zeros within a number are significant.

e.g. 104.6 m (4 s.f. - 1,0,4,6)

Zeros at the end of a number after the decimal point are

significant.

e.g. 2705.0 m (5 s.f. - 2,7,0,5,0)

In a whole number without a decimal point that end inone or more zeroes ..

d


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How long is the red rectangle in centimeters? 4.98 cm

estimated

2 decimal places

How many significant figures? 3

How many millimeters? 49.8 mm


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How Many Significant Figures

0.089 2

1.089 4

12000 2

12001 5

300.0 4

300.01 50.01 1

0.0105 3


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Addition and Subtraction

329.5

23.03

0.083

25.3+

329.5

23.03

0.083

25.3+

329.5

25.3+

0.1rewrite23.0rewrite

377.9


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Multiplication and Division

Result should have the same number of significantfigures as the leastaccurate number

4.03 X 2.4 =9.672 = 9.7

8.55 / 2.399 =3.56398499375 = 3.56

7.0 X 4.70 = 32.9= 33


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Scientific Notation

3.502 x 106

decimal number (0-10)10 raised to aninteger power

Number Significant Figures Scientific Notation

9004 4 9.004 x 103

0.000007 1 7 x 10-6

43 2 4.3 x 101

7,805,000,000 4 7.805 x 109

0.0408 3 4.08 x 10-2

8.4 2 8.4 x 100


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To multiply two numbers in scientific notation multiply the decimal parts of thenumbers and add the exponents algebraically.

(4.0 x 104)(2.0 x 103) =

(4.0 x 2.0)(104

x 103

) =(8.0) x (104+3) =

8.0 x 107


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To divide two numbers in scientific notation, divide the decimal parts of each number thensubtract the exponents.

325

2

5

2

5

10210210

10

2

4

102

104

10646-46-

4

6-

4

10510510510

10

5

25

105

1025


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Experimental Error

Sample data for g (m/s2)

9.70 9.95 9.80 9.65 9.90 9.80

2m/s0.08

6

00.100.1500.150.10

22 m/s0.08m/s9.80g

(0.08/9.8) x 100% 0.8% Accuracy of about 1%

Mean Value -Average of data set is 9.80m/s2

Mean Absolute Deviation

Accuracy


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How many significant figures are there in each of thefollowing?

(i) 0.00042 (ii) 0.14700 (iii) 4.2 x 106

(iv) -154.090 x 10-27

Answers:

Try this....


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How many significant figures are there in each of the following?

(i) 0.00042 (ii) 0.14700 (ii) 4.2 x 106 (iv) -154.090 x 10-27

Answers:(i) 2

(ii) 5

(iii) 2(iv) 6

Try this....


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Table 1.1

Mathematical operation Significant figures in result

Multiplication or division No more than in number with the

fewest significant figurese.g. 0.745 x 2.2 / 3.885=0.42

Addition or subtraction Determined by the number with the

smallest uncertaintye.g.27.153+138.211.74=153.6


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The result of a calculation usually has no moresignificant figures than the input data


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Accuracy and Precision Accuracy:

How close a measurement is to being correct.

Precision:

The number of significant figures (or the uncertainties) in ameasurement.

For gravitational acceleration near the earth,

g = 9.532706 m/s2 and g = 9.7 m/s2.

Which is more(i) precise?

(ii) accurate? (Greater precision does not mean greater accuracy! )
http://localhost/var/www/apps/conversion/tmp/scratch_2/Accuracy%20and%20Precision.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_2/Accuracy%20and%20Precision.ppt

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