lect 1 physics for computer science final.ppt

7/30/2019 lect 1 Physics for Computer Science final.ppt

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Prepared by: CLAYON HARRISON

https://sites.google.com/site/phs1019pfc/
https://sites.google.com/site/phs1019pfc/https://sites.google.com/site/phs1019pfc/


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Assessment

Test 1, 15% Unit 1-4 week 6

Test 2 15% Unit 5-8 week 12

Laboratory Experiments 20%

Final Exam 50 %


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Unit 1: MeasurementUnit 2:Basic MechanicsUnit 3:Oscillations and Waves

Unit4:OpticsUnit 5:Current ElectricityUnit 6:Electromagnetism

Unit 7:ElectronicsUnit 8: Telecommunication


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The system of units used in the scientificcommunity is called the Systemeinternationale .

A Unit is a specified measure of a physicalquantity

The system is based on several fundamentalquantities listed below:


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SI base unit

Base quantity Name Symbol

length meter m

mass kilogram kg

time

second

s

electric current ampere A

thermodynamic temperature kelvin K

amount of substance mole mol

luminous intensity candela cd

When recording measurement you must givenumerical values and the units associatedwith it.


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A fundamental quantity is a quantity fromwhich others can be derived .

Eg. Length and time are fundamentalquantities velocity can be derived fromthem.

L in metres velocity metrestime in seconds second

Velocity is a derived quantity


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Derived unitsQuantity Formula Unit

Area Length x width ?

Volume Length x widthx height

?

density mass/volume ?

Acceleration Velocity/time ?

force mass xacceleration

? N

Work Force x distance ?J

power Work/time ?W


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A scale is a set of marks (graduations) atintervals on a measuring instrument. Thesmaller the value of the subdivisions on scalethe greater the precision

Scales can be said to be linear or non-linear aswell as digital or analogue.

Linear: on a linear scale the marks are equallyspaced


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Non- linear : Marks are not equally spaced

This is an analogue scale


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Low AccuracyHigh Precision High Accuracy Low Precision High AccuracyHigh Precision

Accuracy means how close theexperimental value is to thetrue value

To improve accuracy errors dueto measuring instrumentsand experimental must bereduced

Precision refers to how smallan uncertainty ameasurement instrumentwill give. Example athermometer marked atevery degree will give amore precise reading thanone marked at every fivedegrees.


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Sensitivity speaks about the response of aninstrument to the smallest change in input. Thegreater the response of an instrument to smallchange the more sensitive it is said to be.

Range is the size of the interval between themaximum and minimum quantities that an

instrument can measure.

What is the range of a metre rule?


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The error is the difference between themeasured value and the true value. Thereare two types of errors random andsystematic.

Radom errors are caused by experimentalfactors. Random errors cannot be repeatedexactly .Their effects are normally reducedby taking a number of readings and findingan average. Random errors reduce precision .

Examples : Fluctuations in temp , pressure,

Sudden draughts


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Systematic errors cause readings to beconsistently too high or too low whencompared with the true value. Systematic

errors affect the closeness of measurementto its true value. It reduces the accuracy of the measurements.

Examples: The zero error on a measuringinstrument such as an ammeter


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ABSOLUTE ERROR The absolute error in a quantity is usuallyexpressed in the same unit as the quantityitself. Example: Length of table, L = 1.65 0.05

m. In this case the absolute error L = 0.05 m.

FRACTIONAL ERROR = ABSOLUTE ERRORQUANTITY MEASURED

= .05/1.65 = .0303

PERCENTAGE ERROR = FRACTIONAL ERROR 100%= .0303x100%= 3.03%


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SIMPLE RULES FOR ESTIMATING ACCURACY IN A CALCULATED RESULT

(1)When quantities are ADDED or SUBTRACTED, theirABSOLUTE ERRORS ADD.

(2)When quantities are MULTIPLIED or DIVIDED, theirFRACTIONAL (AND PERCENTAGE) ERRORS ADD.


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In calculating a quantity, y, using the formulay = a + b c, one measures

a = 2.1 0.2 mmb = 1.6 0.1 mmc = 0.50 0.05 mm

Hence, y = 2.1 + 1.6-0.5 = 3.2 mm

Absolute error in y, y = 0.2 + 0.1 + 0.05 = 0.35mm

The result is then y = 3.20 0.35 mm.


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In calculating a quantity, z, using the formulaz= pq

sone measures p = 7.5 0.5 kg

q = 4.0 0.2 ms = 7.0 0.3 m

Hence,

Fractional error in z = fractional error p +fractional error in q + fractional error in s

In symbols z = p +q+ s = 0.5 + 0.2 + 0.3

z p q s 7.5 4 7


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z = (0.067 + 0.05 + 0.043) = 0.16z

Absolute error in z, z = 0.16 z

z = (0.16 4.3) = 0.7 kg

The result is then z = 4.3 0.7 kg


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In calculating a quantity, z, using the formulaz= pq 2

sone measures p = 7.5 0.5 kg

q = 4.0 0.2 ms = 7.0 0.3 m

Hence,

Fractional error in z = fractional error p +2(fractional error in q) + fractional error in s


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In symbols z = p +2q+ s = 0.5 + 2(0.2) + 0.3z p q s 7.5 4 7

z = (0.067 + 2(0.05) + 0.043) = 0.21z

Absolute error in z, z = 0.16 z

z = (0.16 17.14) = 2.74 kg

The result is then z = 17.14 2.74kg


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Problem

Force = mass x accelerationMass = 10 kg 1kg

Acceleration = 2ms -2 0.05ms -2

What is the force?What is the fractional error of the mass?What is the fractional error of the acceleration?What is the percentage error of the force?What is the absolute error of force?


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Factor Prefix Symbol Factor Prefix Symbol

1024 yotta Y 10 -1 deci d

1021 zetta Z 10 -2 centi c

1018

exa E 10-3

milli m1015 peta P 10 -6 micro

1012 tera T 10 -9 nano n

109 giga G 10 -12 pico p

106 mega M 10 -15 femto f

103 kilo k 10 -18 atto a

102 hecto h 10 -21 zepto z

101 deka da 10 -24 yocto y

Sometimes it is necessary to convert sub-multiples (eg.mm) andmultiples(eg.km) to SI units.


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A conversion factor is the factor by which aquantity expressed in one set of units mustbe multiplied in order to be expressed indifferent units.

Example: When converting mm to m theconversion factor is 10 3


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Examples: Larger to smaller1) 1m to mmConversion factor 10 3 Therefore 1m X10 3 =1x10 3mm = 1000mm

2) 1m 2 to mm 2

Conversion factor 10 3

m2 to mm 2(Conversion factor ) 2 = (10 3)2

Therefore 1m 2 X(103)2 = 1 x 10 6 mm 2


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3) 1m 3 to mm 3


m2 to mm 3

(Conversion factor ) 3 = (10 3)3Therefore 1m 2 X(103)3 = 1 x 10 9mm 3

Examples: Smaller to Larger1) 1mm to mConversion factor 10 3 Therefore 1mm 10 3 =1x10 -3m = .001m


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1mm2

to m2


mm 2 to m 2

(Conversion factor ) 2 = (10 3)2

Therefore 1mm 2 (10 3)2 =1 x 10 -6 m2

Now you do it

1mm 3 to m 3


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Zeros shown merely to locate a decimal pointare NOT significant figures example 0.0056Has only 2 significant figures.

When multiplying or dividing numbers, the

number of significant figures in the result isthe same as the least number of significantfigures in any of the multiplied or dividedterms


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Examples:5.000 L

Count all the digits starting at the first non-

zero digit on the left.4 significant figures

0.005 mCount all the digits starting at the first non-

zero digit on the left.1 significant figure


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1.473 2.6

When multiplying or dividing numbers, thenumber of significant figures in the result isthe same as the least number of significantfigures in any of the multiplied or divided

terms.

1.473 has 4 significant figures, 2.6 has only2 significant figures, the result will have 2

significant figures.

1.473 2.6 = 0.57 (rounded up to 0.57 from0.5665 because the number to the right of

the last significant figure was greater than 5)


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Website with applet to try at home.http://www.lon-

capa.org/~mmp/applist/sigfig/sig.htm

Fill in the table

Number/Expression Number of significant figures

987600.0

1+ 0.4212

.002

0.002002

3.211-3.21
http://www.lon-capa.org/~mmp/applist/sigfig/sig.htmhttp://www.lon-capa.org/~mmp/applist/sigfig/sig.htmhttp://www.lon-capa.org/~mmp/applist/sigfig/sig.htmhttp://www.lon-capa.org/~mmp/applist/sigfig/sig.htmhttp://www.lon-capa.org/~mmp/applist/sigfig/sig.htm

lect 1 physics for computer science final.ppt

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