* introduction physical quantities base quantities derived quantities prefixes scientific notation...
TRANSCRIPT
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INTRODUCTION
Physical quantities
Base quantities
Derived quantities
PrefixesScientific notation
(standard form
Scalar quantities
Vector quantities
Dimensional Analysis
CONCEPTUAL MAP
PHYSICAL QUANTITIES
•A quantity that can be measured.•A physical quantities have numerical value and unit of measurement. •For example temperature 30 degrees celcius, 30 is numerical value & ‘degree celcius’ is the unit. Written as 30o C.
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Temperature = 30 degree Celcius = 30o cPhysical quantity = numerical value x unit measurement
1.A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit.
2.The physical quantities can be classified into base quantities and derived quantities.
3.There are seven base quantities: length, mass, time, current, temperature, amount of substance and luminous intensity.
4.The SI units for length, mass and time are metre, kilogram and second respectively.
5.Prefixes are used to denote very big or very small numbers.
BASE QUANTITIES
•Base Quantities are physical quantities that cannot be derived from other physical quantities.•Scientific measurement using SI units (International System Units).
Base Quantities
Symbol SI Unit Symbol of SI unit
Length L meter m
Mass m kilogram kg
Time t second s
Temperature T Kelvin K
Electric current I ampere A
Table 1.1 Shows five base quantities and their respective SI units
Physical Quantities, Units and MeasurementPhysical Quantities, Units and Measurement
T H E M E O N E : M E A S U R E M E N T
C h a p t e r 1
• Vector quantities are quantities that have both magnitude and direction
Magnitude = 100 N
Direction = Left
A Force
Scalars and Vectors
Physical Quantities, Units and MeasurementPhysical Quantities, Units and Measurement
T H E M E O N E : M E A S U R E M E N T
C h a p t e r 1
• Scalar quantities are quantities that have magnitude only. Two examples are shown below:
Measuring Mass Measuring Temperature
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Mass: The amount of matter in a body.
• SI Units: kilogram (kg)
• Common Units:
pounds (lbs) and ounces (oz)
1 kg is approx. 2.2 lbs
1 kg = 1000 g
1 oz = 28.35 g
This Platinum Iridium cylinder is the standard kilogram.
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Length: A measure of distance.
• SI Unit: meter (m)
• Common Units: inches (in); miles (mi)
1 in = 2.54 cm = 0.0254 m
1 mi = 1.609 km = 1609 m
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Volume: Amount of space occupied by a body.
• SI Unit: cubic meter (m3)
• Common Units: Liter (L) or milliliter (mL) or cubic centimeter (cm3)
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Density: Amount of mass per unit volume of a substance.
• SI Units: kg/m3
• Common Units: g/cm3 or g/mL
International systemSI Unit (m K s)
International system(c g s) Unit
International system(f b s) Unit
Measuring Systems
Length
Mass
time
Meter m
Kilogram Kg
Second S
centimeter cm
Gram g
Second S
Foot ft
Bound b
Second S
1.2 SI Units
• Example of derived quantity: area
Defining equation: area = length × width
In terms of units: Units of area = m × m = m2
Defining equation: volume = length × width × height
In terms of units: Units of volume = m × m × m = m3
Defining equation: density = mass ÷ volume
In terms of units: Units of density = kg / m3 = kg m−3
L
W
H
LW
1.2 SI Units
• Work out the derived quantities for:
Defining equation: velocity =
In terms of units: Units of speed = m/s
Defining equation: acceleration =
In terms of units: Units of acceleration = m/s2
Defining equation: force = mass × acceleration
In terms of units: Units of force = Kg m/s2
time
ntdisplaceme
timevelocity
Defining equation: Work = Force x Displacement
In terms of units: Units of Work = J = Kg m2/s2
1.2 SI Units
Defining equation: Energy = Mass x gravity x high
In terms of units: Units of Energy = J = Kg m2/s2
Defining equation: Power = Force x displacement / time
Defining equation: Pressure = Force / area
In terms of units: Units of Power = W = Kg m2/s3
In terms of units: Units of Pressure = Kg m /m2 s2 = Kg m-1/s2 = N/m2
DERIVED QUANTITIIES• Derived Quantities are physical quantities derived from combination
of base quantities through multiplication or division or both
Derived Quantities Symbol Relationship with base quantities Derived units
Area A Length x Length m2
Volume V Length x Length x Length m3
Density ρ MassLength x Length x Length
kg/m3
Velocity v DisplacementTime
m/s
Acceleration a VelocityTime
m/s2
Force F Mass x Acceleration N
Work W Force x Displacement J
Energy Ep
Ek
Mass x gravity x high =½ x mass x velocity x velocity
J
Power P Force x DisplacementTime
W
Pressure p ForceArea
N/m 2
Table 1.2 shows some of the derived quantities and their respective derived units
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Temperature: is the measure of how hot or cold an object is.
• SI Unit: Kelvin (K)
• Common Units: Celsius (ºC) or Fahrenheit (ºF)
Converting between K , ºC and ºF:
TK= TC+273.15
TC= TK – 273.15
TF= 9/5 TC + 32
TC= 5/9 (TF – 32)
“When the thermometer is held in the mouth or under the armpit of a living man in good health” it indicates 98 F
Black board example 19.1
a) What is the temperature in Celsius (centigrade)?
b) What is the temperature in Kelvin?
PREFIXES
• Prefixes :• are used to simplify the
description of physical quantities that are either very big or very small.
Prefix Symbol
Value
Peta P 1015
tera T 1012
giga G 109
mega M 106
kilo k 103
hekto h 102
deka da 10
deci d 10-1
centi c 10-2
milli m 10-3
micro m 10-6
nano n 10-9
pico P 10-12
Femto F 10-15
Table 1.4 Lists some commonly used SI prefixes
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STANDARD FORMStandard form or scientific notation is used to express magnitude in a simpler way. In scientific notation, a numerical magnitude can be written as :
A x 10n, where 1 ≤ A < 10 and n is an integer
Example 1.1 :
For each of the following, express the magnitude using a scientific notation.I.The mean radius of the balloon = 100 mmII.The mass of a butterfly = 0.0004 kg
Solution:
The mean radius of the balloon= 100 mm=100 x 10-3 m = 0.1 m
The mass of a butterfly= 0.0004 kg=0. 0004 x 103 g = 0.4 g
Dimensional Analysis
The word dimension in physics indicates the physical nature of the quantity. For example the distance has a dimension of length, and the speed has a dimension of length/time.
The dimensional analysis is used to check the formula, since the dimension of the left hand side and the right hand side of the formula must be the same.
Example
Using the dimensional analysis check that this equation x = ½ at2 is correct, where x is the distance, a is the acceleration and t is the time.
Solutionx = ½ at2
This equation is correct because the dimension of the left and right side of the equation have the same dimensions.
ExampleShow that the expression v = vo + at is dimensionally correct, where v and vo are the velocities and a is the acceleration, and t is the time Solution The right hand side [v] = L/TThe left hand side L/T + L/T Therefore, the expression is dimensionally correct.
ExampleSuppose that the acceleration of a particle moving in circle of radius r with uniform velocity v is proportional to the rn and vm. Use the dimensional analysis to determine the power n and m.
SolutionLet us assume a is represented in this expression
a = k rn vm
Where k is the proportionality constant of dimensionless unit.The right hand side
n+m=1 and m=2 Therefore. n =-1 and the acceleration a is a = k r-1 v2
k = 1 a= v2/r
Exercise
Part A: See if you can determine the dimensions of the following quantities:
volume acceleration (velocity/time) density (mass/volume) force (mass × acceleration) charge (current × time) Check your answersYou are correct if you wrote down: 1.Volume L3
2.acceleration (velocity/time) L/T2
3.density (mass/volume) M/L3
4.force (mass × acceleration) M·L/T2
5.charge (current × time) I·T
Check youranswers
1.pressure (force/area) M·L-1·T-2
2. (volume)2 L6
3. electric field (force/charge) M·L·I-1·T-3
4. work (in 1-D, force × distance) M·L2/T2
5.energy (e.g., gravitational potential energy = mgh = mass × gravitational acceleration × height)
M·L2/T2
6. square root of area L
Part B: Now find the dimensions of these: 1.pressure (force/area) 2.(volume)2 3.electric field (force/charge) 4.work (in 1-D, force × distance) 5.energy (e.g., gravitational potential energy = mgh6.square root of area
Which one of the following quantities are dimensionless?
1-68 2-sin (68 ) 3-e 4-force 5-6 6-frequency 7-log (0.0034)