Phy110 - Chapter 1

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CHAPTER 1Physical Quantities6 Hours)

Prof. Madya Dr. Ahmad Taufek Abdul RahmanSchool of Physics & Material Sciences

Fakulty of Applied Sciences

Universiti Teknologi MARA Malaysia

Campus of Negeri Sembilan

72000 Kuala Pilah

Negeri Sembilan, Malaysia

AS120

Diploma in Science

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DR.ATAR @ UiTM.NS PHY110 2

Chapter Outline1.0 Physical Quantities

1.1 Measurement1.2 Units and standards of measurements1.3 Unit conversion

(Dimension Analysis Not Included)

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1.1 Measurement

Science and Engineering are Based onMeasurements and Comparisons

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1.1 MeasurementWhat is measurement?

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1.1 MeasurementWhat is measurement?

Measurement is the processthat brings a precisionto a description by specifying the howmu handofwh tof a quantity in particular situation.A number expresses the valueof the quantity, andthe name of a unit tells you what the referentis aswell as implying the procedure for obtaining thenumber.

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1.1 MeasurementHow do we measured the quantities?

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1.1 MeasurementHow do we measured the quantities?

The measurement was made using theappropriateness of the measuring instruments

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1.1 MeasurementDo you think your measurement is correct?

No Because every measurement made has anuncertainty that is determined by the precision ofthe apparatus used and the physical constraints ofindividual.

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1.1 MeasurementAccuracy and Precision

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Physics demands accurate and precise measurement.

Low Accuracy

High Precision

High Accuracy

Low Precision

High Accuracy

High Precision

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Physics demands accurate and precise measurement.Accuracy is how close a measured value is to theactual (true) value.

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Physics demands accurate and precise measurement.

Precision is how close the measured values are toeach other.

Accuracy is how close a measured value is to theactual (true) value.

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SI unit of length is meter (m) Tools of measurement meter rule, vernier calipersand micrometer screw gauge Do not measure something using equipment which not

according to its specification Because every measurement instrument has finiteamount of accuracy

Meter rule - 0.1 cmVernier caliper - 0.01 cmMicrometer screw gauge - 0.01 mm

Measurement of Length

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Figure 2

Meter Rule

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Was the end of the object exactlyopposite the zero of the ruler?

reading the smallest division on the measuring instrument

Meter Rule

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Vernier Scale

A vernier scale is a small, moveable scale placednext to the main scale of a measuring instrument. It is named after its inventor, Pierre Vernier(1580

- 1637). It allows us to make measurements to a precisionof a small fraction of the smallest division on themain scale of the instrument. There are two specifics examples vernier calipersand micrometer screw gauge

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Vernier Calipers

Vernier calipers can measure up to an accuracy of0.01 cm.

Vernier calipers are used to measure the internaland external diameters of tubes and length of asmall object.

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0.1 cm

External Caliper

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0.1 cm

Internal Caliper

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Vernier Calipers

0.01 cm

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Digital Vernier Calipers

0.01 mm

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Reading Vernier Calipers Scale

The figure shows a Vernier scale reading zero. Noticethat 10 divisions of the Vernier scale have the samelength as 9 divisions of the main scale. We will assume that the smallest division on the mainscale is 0.1 cm so the divisions on the Vernier scaleare 009 cm each.

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1.Check for zero errorZero error: - the zero of the vernier scale does notcoincide with the zero of the main scale when thejaws is closed (has no object measured).

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2. Read the main scaleTake the reading from the main scale up to the markjust before the zero line of the vernier scaleGive the reading (in cm) up to the one decimal point

Main scale = 2.6 cm

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3.Read the vernier scaleTake the mark from the vernier scale which coincideswith the line on the main scale.Gives the reading with two decimal places.

Vermeer scale = 0.07 cm

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Final reading = (2.6 cm + 0.07 cm) - 0 = 2.67 cm

Final reading = (main scale + vernier scale) Zero Error


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Reading Micrometer Screw Gauge

0.01 mm

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2.Read the Sleeve ScaleTake the reading on the sleeve scale up to theedge of the thimble. The sleeve scale gives thereading in mm with one decimal place.

Sleeve scale = 3.5 mm

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3. Read the Thimble ScaleThen take the thimble scale reading at the markwhich coincides with the datum line.The thimble scale gives the reading (in mm)with two decimal places.

Thimble scale = 0.22 mm

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The final reading = (3.5 mm + 0.22 mm) - 0 = 3.75 mm

Final reading = (sleeve scale + thimble scale) Zero Error


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EXERCISES

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EXERCISES

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EXERCISES

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EXERCISES

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EXERCISES

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EXERCISES

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EXERCISES

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EXERCISES

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EXERCISES

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EXERCISES

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EXERCISES

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Error AnalysisType of ErrorsRandom Errorsare usually small and has equalprobability of being positive or negative, example;

parallax error (an error due to incorrect eyesposition during the measurement), mistake inmeasurement, wrong count etc.Systematic ErrorsConstant error due toinstruments, physical conditions of the surroundingor physical limitation of the observer.

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Error AnalysisDetermination of Uncertainty

Let say the length of solid is written as l = (67.55 0.05) cmTherefore:-

Absolute error = l = 0.05 cmRelative error =

Percentage error =l

l

100)(l

l

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Error AnalysisDetermination of Uncertainty

Added or subtracted their absolute errors aresummed

Multiplied or divided, their percentage error aresummed Power of n, the percentage error is multiplied by n

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Significant Figures The significant figures in a number are allfigures that are obtained directly from themeasuring process and exclude those zeroswhich are included solely for the purpose oflocating the decimal point. A measurement and its experimental errorsshould have their last significant digits in thesame location

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Significant Figures When adding or subtracting numbers, the number ofdecimal places of the answer must be equal to the least

number of decimal places of the given numbersExample:a) 26.2 cm + 5.67 cm = ________________b) 3.05 cm 0.528 cm = ________________

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Exercises

2. To measure the mass of water in a beaker, thefollowing reading were taken.Mass of empty beaker, m1 = (45.6 0.5) gMass of beaker and water, m2 = (82.8 0.5) ga) What is the absolute error and percentage error of themass of the water.b) How would the mass of the water be recorded as?

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Exercises

3. A cyclist take 15.78 s to travel a distance of 125 m.what is his average speed? Give your answer to thecorrect number of significant figures.

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Graph Plotting a graph is one way to find the relationshipbetween measured variables. The most important quantities that are deducedfrom a straight line graph are:

i. Gradient of the graph, mii. Intercepts on the axes, c

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Information from the Graph

y = mx + c

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Plotting Graph1. Use s sharp pencil to avoid any unnecessary inaccuracies2. Draw your graph on a full page of the graph paper (> of graph paper)3. Give the graph a concise title4. The dependent variable should be plotted along thevertical axis (y) and the independent variable along thehorizontal axis (x)5. Label axes include units6. Select the best scale and start at zero if possible7. Use error bar to indicate errors in measurements8. Draw a smooth curve through the data point (best line aspossible about 2/3 of the data plot lie along the curve)

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Analysis Graph1. Calculate and coordinates of the centroid.

n

y

n

x ii ,

2. The best straight line of the graph that is drawnmust pass through the centroid.3. Draw another straight line, one with the maxgradient (mmax) and second with the least gradient(mmin). These two straight line must be pass throughthe centroid.

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Errors in Graph1. Relative uncertainty of intercept c

c

cc

c

c minmax

2

1

2. Relative uncertainty of gradient m

m

mm

m

mminmax

2

1

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Examples

1. Graph the data using the above guidelinesSpeed (m/s) Time (s)

0.45 0.06 1

0.81 0.06 2

0.91 0.06 3

1.01 0.06 4

1.36 0.06 5

1.56 0.06 6

1.65 0.06 71.85 0.06 8

2.17 0.06 9

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Examples

2. A cyclist starts from rest and the distance travelled ismeasured as a function of time. The time measurement isassumed to be precise. Determine distance d as a function oftime t by graphical analysis.Distance (m) Time (s)

1.2 0.6 1

5.4 0.6 2

11.1 0.6 3

22.0 0.6 4

32.1 1.0 549.0 1.0 6

63.1 1.5 7

86.0 1.5 8

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1.2 Physical Quantities and Units Physical quantity is defined as a quantity which can

be measured.

It can be categorised into 2 types

Basic (base) quantity

Derived quantity

Basic quantity is defined as a quantity which cannot

be derived from any physical quantities.

Derived quantityis defined as a quantity which can be

expressed in term of base quantity.

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Basic Quantities and UnitsQuantity Symbol SI Unit Symbol

Length l metre m

Mass m kilogram kg

Time t second sTemperature T/ kelvin K

Electric current I ampere A

Amount of substance N mole mol

Luminous Intensity candela cd

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Derived Quantities and UnitsDerived quantity Symbol Formulae Unit

Velocity v s/t m s-1

Volume V l w t M3

Acceleration a v/t m s-2

Density m/V kg m-3

Momentum p m v kg m s-1

Force F m a kg m s-2 @ N

Work W F s kg m2

s-2

@ J

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ATAR@UiTM/PHY081/1 64

meterThe meter was again redefined in 1983 as

the length of the path traveled by light in

vacuum during a time interval of

1/299,792,458 of a second.

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kilogramThe SI unit of mass.1 kg is equal to themass of aninternational prototypemetal cylinder by aplatinum-iridium alloycylinder.

The standard ki logram

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Second was redefined in 1967 in terms of theresonant frequency of the cesium atom-thatis, the frequency at which this atom absorbsenergy, or a duration of 9,192,631,770period of radiation emitted by cesium 133atom.

second

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KelvinThe SI unit of temperature.It is equal to 1/273.16 of thetemperature of the triple point of water,at which the solid, liquid, and gas are inequilibrium can all exist at the sametime) on the absolute temperature scale.

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The SI unit of current .The ampere A) was defined as the constantcurrent that, flowing in two parallelconductors one meter apart in a vacuum, willproduce a force between the conductors of 2

10 -7Newton per meter of length.1 A of current is equivalent to 1 C of chargepassing through the cross-sectional area in atime interval of 1s.

1 A=1 Cs-1

Ampere

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Units Unit is defined as a standard size of measurement of physical

quantities. The common system of units used today are S.I unit

(System Internat ional/metr ic syst em)

Examples :

1 second is defined as the time required for 9,192,631,770

vibrations of radiation emitted by a caesium-133 atom.

1 kilogram is defined as the mass of a platinum-iridium

cylinder kept at International Bureau of Weights and

Measures Paris.

1 meter is defined as the length of the path travelled by light

in vacuum during a time interval of

s458,792,299

1

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Unit Prefixes It is used for presenting larger and smallervalues. Unit prefixes is important to express largerand smaller units in the same physicalquantities. The names of the additional units are derived

by adding a prefix to the name of thefundamental unit.

UNIT PREFIXES

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Power Prefix Abbreviat ion10-18 Atto a10-15 Femto f10-12 Pico p10-9 Nano n10-6 Micro 10-3 Mil i m10

-2Centi

c

10-1 Deci d101 Deca da103 Ki lo k106 Mega M109 giga G1012 tera T1015 peta P1018 exa E

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1.3 Conversion of UnitsLength Mass

1 m = 39.37 in = 3.281 ft 1 kg = 103 g

1 in = 2.54 cm 1 slug = 14.59 kg1 km = 0.621 mi 1 lb = 0.453 592 kg

1 mi = 5280 ft = 1.609 km 1 kg = 0.0685 slug

1 angstrom () = 1010 m

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Example1. Solve the following problems of unitconversion.

a) 30 mm2= ? m2b) 865 km h1= ? m s1c) 300 g cm3= ? kg m3d) 17 cm = ? Ine) 24 mi h1= ? km s1

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Solution

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Solution

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Solution

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Thank You

Phy110 - Chapter 1

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