lect 1 Physics for Computer Science final.ppt
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Transcript of 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
Conversion factor 10 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
Conversion factor 10 3
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