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 Safe Hands, Akola

Need of system of units It must be convenient Easily reproducible Must be uniform and constant Internationally accepted. Safe Hands, Akola

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. Safe Hands, Akola

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 Safe Hands, Akola

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 Safe Hands, Akola

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. Safe Hands, Akola

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. Safe Hands, Akola

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, Safe Hands, Akola

Derived physical quantities Speed length/time m/s Acceleration length/time2 m/s2 Density mass/ length3 kg/m3 Volume length3 m3 Force mass.(length)/time2 kg.m/s2 Momentum mass. Length/time kg. m/s Pressure mass/length.time2 kg/ms2 room temperature temperature K Safe Hands, Akola

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 Safe Hands, Akola

Derived physical quantities Charge = current x Time = A.s Work = 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 Safe Hands, Akola

Fundamental Quantities More about Units Fundamental Quantities SI Units Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Luminous intensity candela cd Temperature kelvin K Mole mole mol Safe Hands, Akola

More about Units Derived Quantities SI Units Symbol Force newton N Work / Energy joule J Power watt W Electric charge coulomb C potential volt V resistance ohm Ω frequency hertz Hz Safe Hands, Akola

Always remember - - - Newton n kg Kg Full names of units are NOT written starting with capital initial letter. Kilogram Meter meter 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. n newton N kg kilogram Kg Safe Hands, Akola

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. Safe Hands, Akola

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] acceleration [L1T-2] Electric charge [IT] momentum [M1L1T-1] Force [M1L1T-2] Density [M1L-3] Work/ Energy [M1L2T-2] Radian, refractive index etc [ ] Power [M1L2T-3] Safe Hands, Akola

Application of dimensional equation Dimensional analysis can be used — to check whether the given equation is dimensionally correct. ( If an equation is dimensionally correct then it can differ only in numerical constants.) 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 c = 10000 = 105 Safe Hands, Akola

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 : Doubtful figure: 4.8 4.85 0 1 2 3 4 Safe Hands, Akola

Significant figure Significant figure: The number of all nonzero digits are significant. 234 has 3 significant digits 17065001 has 8 significant digits 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 200 has 1 significant digit 3700 has 2 significant digits 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 has 3 significant digits 0.0120 has 3 significant digits 0.00 has 2 significant digit 0.000012 has 2 significant digits Safe Hands, Akola

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. Safe Hands, Akola

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 Safe Hands, Akola

Multiples and divisors Prefix Symbol Multiples deca da 10 hecto h 102 kilo k 103 mega M 106 giga G 109 tera T 1012 peta P 1015 exa E 1018 zetta Z 1021 yotta Y 1024 Prefix Symbol Multiples deci de 10-1 centi c 10-2 milli m 10-3 micro  10-6 nano n 10-9 peco p 10-12 femto f 10-15 atto a 10-18 zepto z 10-21 yocto y 10-24