Transcript Mechanics and properties of matter Measurements By: Dr. Nitin Oke. Safe Hands, Akola Need of measurement • Physical theory need experimental verification and results of experimental verification involves measurement. •

Mechanics
and
properties of matter
Measurements
By: Dr. Nitin Oke.
Safe Hands, Akola
Need of measurement
• Physical theory need experimental
verification and results of experimental
verification involves measurement.
• If every one decide to have his own way
of measurement then it will not be
possible to come to correct conclusion.
• Thus a well defined, universally accepted
system must be developed
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Need of system of units
•
•
•
•
It must be convenient
Easily reproducible
Must be uniform and constant
Internationally accepted.
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Different systems of units
• FPS system: Used by Europeans, consist
of three basic units for length, mass and
time. The units were foot (ft), pound (lb)
and for time it is second (s).
• Metric system: MKSA system, it is system
based on quantities for length, mass, time
and current. Sub system of this system is
more popular by name MKS.
• SI system: Recent mostly accepted. It is
abbreviation of ”System International de
unites” (1960) It consist of six base units
two supplementary units and derived units.
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SI system
• Base units are
– Meter : it is defined as 165076373 times the
wavelength in vacuum of orange red line emitted by
krypton 86.
– Present definition is length of path traveled by light
in vacuum during time interval 1/299792458 of
second.
– Kilogram : It is the mass of prototype of iridium –
platinum alloy kept in “ International Bureau of
Weights and measures at serves, Near Paris in France
– Second : It is the time taken by radiation from
cesium- 133 atom to complete 9192631770 vibrations
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SI system
• Base units are
– Ampere : it is defined as current flowing through
each of two thin parallel conductors of infinite length
kept in free space at a distance of a meter apart,
produces a force of 2 x 10-7 N per unit length.
– Candela : It is the luminous intensity of an area of
1/600000 m2 of black body in the normal direction to
its surface at temperature of freezing platinum
under the pressure of 101325 N/m2
– Kelvin : It is the fraction 1/ 273.16 of
thermodynamic temperature of triple point of water.
– Mole : It is defined as the amount of substance of a
system which the same number of elementary entities
as there are atoms in exactly 12 grams of pure
carbon 12
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SI system
• Supplementary units are
– Radian : It is the angle subtended by an
arc length equal to radius of a circle at
centre of circle.
– Steradian : It is the solid angle
subtended at the centre of a sphere by
an area of a square on the surface of a
sphere each side of square is of length
equal to radius of sphere.
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Fundamental physical quantities
• Fundamental physical quantities: The
physical quantities which can not be
expressed in terms of other physical
quantities are called as fundamental
physical quantities.
• Fundamental physical quantities: The
physical quantities which are chosen for
base units are called as fundamental
physical quantities.
• Fundamental units: Units expressing
fundamental quantities is called as
fundamental units.
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Derived physical quantities
• Physical quantities which can be
expressed in terms of one or more
fundamental quantities are called as
derived quantities.
– Speed , acceleration, density, volume, force,
momentum, pressure, room temperature.
charge, potential difference, KE, PE,
resistance, work,
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Derived physical quantities
–
–
–
–
–
–
–
–
Speed
length/time
Acceleration
length/time2
Density
mass/ length3
Volume
length3
Force
mass.(length)/time2
Momentum
mass. Length/time
Pressure
mass/length.time2
room temperature temperature
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m/s
m/s2
kg/m3
m3
kg.m/s2
kg. m/s
kg/ms2
K
Short recall
•
•
•
•
•
•
Force = mass. displacement
Work = force . Displacement
KE = ½ mv2
PE = m. g. h
I = charge/time
pd = energy required to circulate the unit
charge from terminal to terminal. = E/q
• R = V/I
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Derived physical quantities
– Charge
– Work
–
–
–
–
–
= current x Time = A.s
= force . Displacement
= mass x (length)2/(time)2
KE
= mass x (length)2/(time)2
PE
= mass x (length)2/(time)2
potential difference
= energy per unit charge
= [mass x (length)2/(time)2] /current. time
= mass x (length)2 /current. time3
Resistance
= V/ I = (M.L2/I.T3)/I = ML2/I2T3
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More about Units
Fundamental
Quantities
Length
meter
m
Mass
kilogram
kg
Time
second
s
ampere
A
candela
cd
Temperature
kelvin
K
Mole
mole
mol
Electric
current
Luminous
intensity
SI Units
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Symbol
More about Units
Derived
Quantities
Force
SI Units
newton
Symbol
N
Work / Energy joule
J
Power
W
watt
Electric charge coulomb
C
potential
volt
V
resistance
ohm
Ω
frequency
hertz
Hz
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Always remember - - • Full names of units are NOT written
starting with capital initial letter.
Meter
meter
Kilogram kilogram
Newton
newton
Units named after person will NOT be written with
capital initial letter. The symbol of the units in
memory of a person will be in capital letters. This will
not be for other units.
newton N
kilogram Kg
n
kg
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Dimensional Analysis
• Dimensions of a physical quantity are the powers
to which the fundamental units must be raised
in order to get the unit of derived quantity.
– Symbols used for fundamental quantities are
– Length [ L ] , mass [ M ], time [ T ], current [I],
Temperature [  ]
– Using powers of these symbol we represent dimension
of physical quantities.
• In short the dimension is expression which
shows the relation between the derived
unit and the fundamental units.
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Dimensions of derived units
Derived
Quantities
dimension
Derived
Quantities
dimension
frequency
[T-1]
potential
[M1L1T-3 I-1]
speed
[L1T-1]
resistance
[M1L1T-3 I-2]
[IT]
acceleration [L1T-2]
momentum
[M1L1T-1]
Electric
charge
Force
[M1L1T-2]
Work/
Energy
Density
[M1L-3]
[M1L2T-2]
Power
[M1L2T-3]
Radian,
refractive
index etc
[]
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Application of dimensional equation
•
Dimensional analysis can be used —
1.
to check whether the given equation is dimensionally
correct. ( If an equation is dimensionally correct
then it can differ only in numerical constants.)
2. To find the relation between same unit in different
systems. For example
let 1N = c dyne
1[M1L1T-2] = c [M1L1T-2]
kg.m.s-2
= c gm.cm.s-2
kg m s2

 2 c
gm cm s
c  10000  105
1000gm 100cm

1  c
gm
cm
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Significant figure
• Order of magnitude: If a number is
expressed as “n x 10m ” where 0.5 ≤ n < 5
then 10m is called as order of magnitude.
• Significant figure:
– Reliable figure :
4.8
– Doubtful figure:
4.85
0
1
2
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3
4
Significant figure
• Significant figure:
• The number of all nonzero digits are significant.
– 234
– 17065001
has 3 significant digits
has 8 significant digits
– 200
– 3700
has 1 significant digit
has 2 significant digits
–
–
–
–
has 3
has 3
has 2
has 2
• Decimal point is a problem as
• If number is free of decimal point then zero on right of
first nonzero digit are NOT significant means
• If number is with decimal point then zeros to the right
of decimal point and on left of first nonzero number is
non significant but zeros on right of last nonzero digit
are significant
0.0102
0.0120
0.00
0.000012
significant digits
significant digits
significant digit
significant digits
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Need and notation of scientific numbers
• If reading is
• 2.320m = 232.0cm = 2320mm =0.002320km
• Here 2320mm has 3 significant digits and 2.320
has 4 significant digits
• To avoid above contradiction we use scientific
notation in which the number will be written as
– 2.320m = 2.320 x 102cm
= 2.320 x 103mm = 2.320 x 10-3km
• As power of ten does not contribute in
significant figures thus even by changing units
the number of significant digits will remain
same.
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Operation with scientific figures
• During addition or subtraction always express
answer with number of digits after decimal point
is same as the number with the least number of
digits after decimal point.
• For example
987.231
+ 34.3
+456.096
1477.6
1477.627
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Multiples and divisors
Prefix
Symbol
deca
hecto
kilo
mega
giga
tera
peta
exa
zetta
yotta
da
h
k
M
G
T
P
E
Z
Y
Multiples
Prefix
10
102
103
106
109
1012
1015
1018
1021
1024
deci
centi
milli
micro
nano
peco
femto
atto
zepto
yocto
Symbol
de
c
m

n
p
f
a
z
y
Multiples
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24