MEASUREMENTS

Course: Diploma

Subject: Applied Science Physics

Unit: I

Chapter: I

MEASUREMENTS

Necessity of Measurement

• Representation of Physical Quantity Physical Quantities

• Measurable &Understandable• Not Observable, non touchable

e.g. Length, Mass, Time, Speed, Acceleration, Force, Work, Pressure

• Tow types Concrete-Mass, Abstract-Heat

CONCEPT OF UNIT OF A PHYSICAL QUANTITY

What is unit ?• Unit is standard of physical quantity• Independent of physical & environmental

condition• Three Types

1. The Fundamental Units

2. Derived Units

3. Practical Units

THE FUNDAMENTAL UNITS

Length meter m Mass Kilogram kg Time Second s Electric current Ampere A Thermodynamic temp Kelvin K Amount of a substance mole mol Luminous Intensity Candela Cd

DEFINITIONS

The Meter :- the distance traveled by a beam of light in a vacuum over a defined time interval ( 1/299 792 458 seconds)

The Kilogram :- a particular platinum-iridium cylinder kept in Sevres, France

The Second :- the time interval between the vibrations in the cesium atom

(1 sec = time for 9 192 631 770 vibrations)

Table 1: SI Prefixes Larger & smaller units defined from Greek prefixes

Factor Decimal Representation Prefix Symbol1018 1,000,000,000,000,000,000 exa E

1015 1,000,000,000,000,000 peta P

1012 1,000,000,000,000 tera T

109 1,000,000,000 giga G

106 1,000,000 mega M

103 1,000 kilo k

102 100 hecto h

101 10 deka da

100 1

10-1 0.1 deci d

10-2 0.01 centi c

10-3 0.001 milli m

10-6 0.000 001 micro m

10-9 0.000 000 001 nano n

10-12 0.000 000 000 001 pico p

10-15 0.000 000 000 000 001 femto f

10-18 0.000 000 000 000 000 001 atto a

TYPICAL LENGTHS (APPROX.)

1

TYPICAL TIMES & MASSES (APPROX.)

2

THE DERIVED UNITS The International System of Units (SI) specifies

a set of seven base units from which all other SI units of measurement are derived.

For example, the SI derived unit of area is the square meter (m2), and the SI derived unit of density is the kilogram per cubic meter (kg/m3 or kg m−3)

Derived Units(Named units derived from SI base units)

Name Symbol Quantity Equivalents SI base unit

hertz Hz frequency 1/s s−1

radian rad angle m/m dimensionless

steradian sr solid angle m2/m2 dimensionless

newton N force, weight kg m/s2⋅ kg m s−2⋅ ⋅

pascal Pa pressure, stress N/m2 kg m−1 s−2⋅ ⋅

joule J energy, work, heat N m⋅ kg m2 s−2⋅ ⋅

watt W power, radiant flux J/s kg m2 s−3⋅ ⋅

coulomb C electric charge or quantity of electricity s A⋅ s A⋅

volt Vvoltage, electrical potential difference, electromotive force W/A kg m2 s−3 A−1⋅ ⋅ ⋅

farad F electrical capacitance C/V kg−1 m−2 s4 A2⋅ ⋅ ⋅

ohm Ω electrical resistance, impedance, reactance V/A kg m2 s−3 A−2⋅ ⋅ ⋅

siemens S electrical conductance 1/Ω kg−1 m−2 s3 A2⋅ ⋅ ⋅

weber Wb magnetic flux J/A kg m2 s−2 A−1⋅ ⋅ ⋅

tesla T magnetic field strength, magnetic flux density V s/m2⋅ kg s−2 A−1⋅ ⋅

henry H Inductance V s/A⋅ kg m2 s−2 A−2⋅ ⋅ ⋅

PRACTICAL UNITS

Physical Quantity Unit Symbol

Current Ampere A

Electric Charge Coulomb C

Capacitance Farad F

Inductance Henry HEnergy Joule J

Resistance Ohm Ω

Voltage Volt V

Power Watt W

units of magnitudes convenient for use in the practical applications of electricity; as originally defined they were absolute units they include the ampere, coulomb, farad, Henry, joule, ohm, volt, and watt.

STANDARDS OF MEASUREMENT UNITS

Scientists and engineers need to make accurate measurements so that they can exchange information

To be useful a standard of measurement must be Invariant, Accessible and Reproducible

Internationally Usable

VARIOUS SYSTEMS OF UNIT CGS System- Centimeter, Gram, Second MKS System- Meter, Kilogram, Second FPS System – Foot, Pound, Second Standard International Unit System- MKS

system is used as SI• Uses internationally• All Engineering & Technology

CONVERSIONS You will need to be able to convert from one unit

to another for the same quantityJ to kWhJ to eVYears to secondsAnd between other systems and SI

KWH TO J

1 KWh = 1kW x 1 h = 1000W x 60 x 60 s = 1000 Js-1 x 3600 s = 3600000 J = 3.6 x 106 J

YR TO SEC 1 year = 365 days OR 1 year

= 365 *24 Hrs = 365*24*3600 Sec

= 8760 Hrs = 31536000 Sec

= 8760 * 60 Minutes

= 525600 Minutes

= 525600 * 60 Sec

= 31536000 Sec

J TO EV 1 eV = 1.6 x 10-19 J

UNIT CONVERSION Example: Is he speeding ?

On the garden state parkway of New Jersey, a car is traveling at a speed of 38.0 m/s. Is the driver exceeding the speed limit?

Put 1’s using unit conversion relations, as many times as necessary. Multiply or divide numbers and units. Begin with 38.0 m/s = (38.0 m/s) 1 Since 1 mile = 1609 m, so we have 1 = 1 mile/1609 m Then

Finally

3

OTHER UNITS TO SI CONVERSIONS CGS TO SI 1cm = 1/100 m 1000 g = 1Kg 1 sec = 1 seco Velocity In CGS cms-1= In SI 10-2 ms -1

Force,1N = kgms -2 In SI = 105 dyne In CGS

SI FORMAT

The accepted SI format isms-1 not m/sms-2 not m/s/s

i.e. we use the suffix not dashes

Quantities have dimensions: Length – L, Mass – M, and Time - T

Quantities have units: Length – m, Mass – kg, Time – s

DIMENSIONS, UNITS AND EQUATIONS

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DIMENSIONS AND DIMENSIONAL ANALYSIS Dimension – It is useful to consider physical

dimension because it provides a way to track what symbols mean through long calculations—a process known as dimensional analysis.

Physical quantity

Unit Dimension

Area m2 L x L = L2

Velocity m s-1 L/T = L T-1

Acceleration

m s-2 L T-1/T = L T-2

Force N = kg m s-2 M L T-2

Work J = kg m2 s-2 M L2 T-2

DIMENSIONAL ANALYSIS

Fundamental rules: All terms in an equation must reduce to identical primitive dimensions

Dimensions can be algebraically manipulated, e.g.

Example:

Uses: Check consistency of equations Deduce expression for physical phenomenon

2

2

2

1s at

2

TL* L

T

Dimensional analysis

distance s = s0 +vt2 + 0.5at3

constant = p + ρgh +ρv2/2

volume of a torus = 2π2(Rr)2

REFERENCE BOOKS AUTHOR/PUBLICATION

ENGINEERING PHYSICS S S PATEL (ATUL PRAKASHAN)

MODERN ENGINEERING PHYSICS A S VASUDEVA

ENGINEERING PHYSICS K. RAJGOPALAN

FIGURE REFERENCE LINKS

1. http://nothingnerdy.wikispaces.com/1+Physics+and+physical+measurement

2. http://imgur.com/RZ7N0dh

3. http://imgur.com/lIksNhq

4. http://imgur.com/dYH9p91

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