chapter-1
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CHAPTER-1. Measurements. Chapter 1- Measurement. Topics to be covered : Measurement of a physical parameter Units, systems of units Basic units in mechanics Changing units Significant figures. Ch 1-2 Measuring Things. Units and Standards. - PowerPoint PPT PresentationTRANSCRIPT
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CHAPTER-1
Measurements
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Chapter 1- Measurement
Topics to be covered :
Measurement of a physical parameter
Units, systems of unitsBasic units in mechanicsChanging unitsSignificant figures
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Ch 1-2 Measuring Things Units and Standards. Measurements of Physical quantity
in unit in comparison with a standard.
Each Physical Quantities has its associated unit and a standard to compare with
Base Physical Quantities : Length (L) , Mass (M) and Time (T) Derived Physical Quantities: speed = length/time acceleration = speed/time force = mass x acceleration
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Ch 1-2 Measuring Things
Base Unit associated with base quantities
Derived Units associated with derived quantities
Base-Standards associated with base physical quantities
Derived-Standards associated with derived quantities
Base Unit Systems International System (mks) Gaussian System (cgs) British engineering system (fps)
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Table of Base Units System
System Length Mass Time
SI(mks) meter (m) kilogram(kg)
second(s)
Gaussian (cgs) centimeter(cm)
gram (g) second(s)
British (fps) foot (ft) slug*pound
second(s)
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Prefix
A multiplier of a unit to increase or decrease its value
Prefix in SI units given in terms of power of tens
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Prefix for SI units
Factor Prefix Symbol
1012 tera T
109 giga G
106 mega M
103 kilo k
10-2 centi c
10-3 milli m
10-6 micro 10-9 nano n
10-12 pico p
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Ch 1-4 Changing Units
Changing units using Chain-link conversion
Multiplication of original measurement by a conversion factor c
Change of 5 min into seconds Conversion factor c = 60 s/1 min 5 min= 5 min x c = 5 min x (60 s/1
min)=300 s Conversion factor c for changing
year into seconds c =(365 days/1year)x(24 h/1day) x (60 min/ 1 h) x (60 s/1 min)
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Significant Figures
Precession in data given by Significant Figures
Significant Figures (SF): number of digits in a number,
33 m/s has two digits hence two SF
1.33 m has three SF Final Result of a calculation
cannot be more precise than the least significant figure in the data
Z = A(2 SF) x B(3 SF) Z will be rounded off to have 2SF
number
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Standards -SI units system
SI (mks) Unit System
Length Mass Time
meter (m) kilogram (kg) second (s)
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The Meter A
C
B
Earth
Equator
In 1792 the meter was defined to be one ten-millionth of the distance from the north pole to the equator.
The meter was later defined as the distance between two fine lines on a standard meter bar made of platinum-iridium.
Since 1983 the meter is defined as the length traveled by light in vacuum during the time interval of 1/299792458 of a second.
The measurement of the speed of light had become extremely precise.
71 m
10
AB
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Ch 1-5 Length
SI unit of length-meter Length of a platinum-iridium bar
(standard meter bar) kept at International Bureau of Weights and Measures near Paris
The meter is the length of the path traveled by light in a vacuum during a time interval of 1/299792458 of a second:
speed of light c =299 792 458 m/s
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The SecondInitially the second was defined as follows:
The length of the day is not constant as is shown in the figure.
Since 1967 the second is defined as the time taken by 9192631770 light oscillations of a particular wavelength emitted by a cesium-133 atom.
it would take two cesium clocks 6000 years before their readings would differ by more than 1 second.
11 second
24 60 60of the time it takes the Earth
to complete a full rotation
about its axis.
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Ch 1-6 Time
SI unit of time-secondTime measurement with
reference to frequency (9 192 631 770 Hz) of light emitted by cesium-133 atom (atomic clock)
One second is the time taken by 9 192 631 770 oscillations of light emitted by a cesium-133 atom
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The Kilogram
The SI standard of mass is a platinum-iridium cylinder shown in the figure. The cylinder is kept at the International Bureau of Weights and Measures near Paris and assigned a mass of 1 kilogram. Accurate copies have been sent to other countries.
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Ch 1-7 Mass
SI unit of mass-kilogram Mass of a platinum-iridium cylinder
(The Standard kilogram) kept at International Bureau of Weights and Measures near Paris.
Second Mass Standard Atomic mass unit (amu): 1 amu = 1.6605402 x 10-27 kg Mass of C-12 atom = 12
amu
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Dimensional Analysis
Dimension denotes qualitative nature of a physical quantity
Symbols L, M, T are used to specify length, mass and time nature of a physical quantity respectively.
The brackets [ ] are used to denote the dimension of a physical quantity
[velocity v] = L / T ; [Area A] = L2
Dimensions are treated as algebraic quantities and can be multiplied or divided mutually
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Dimensional Analysis
Dimensional Analysis is used to check a formula
A formula is correct only if the dimension of both side of the relationship are same.
Example: Acceleration of a particle moving in a circle is given by : a=krnvm
Determine the values of constant k and exponents n and m
The dimensional equation is L/T2=Ln(L/T)m=Ln+m/Tm
Equating exponents of L and T separately:
1=n+m; 2=m; m=2; n=1-m=1-2=-1 Then L/T2 = k L/T2 ; and k=1
Hence a=krnvm = r-1v2 = v2/r
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Thank you