
PSUT- Basic Science Department

Omar Zayed
CHAPTER ONE
PHYSICS AND
MEASUREMENTS
CHAPTER ONE
Physics and Measurements
Description of the Chapter
Name of the course
20141, Physics (1)
Number of the chapter
Chapter 1
Title of the chapter
Physics and Measurements
Objectives of the unit
Objectives:
At the end of this chapter, students should be able :
•
To define standards of length , mass and time
•
To classify Physical quantities into fundamental quantities and derived quantities
•
To use the prefixes in physics .
•
To define the ( model ) in physics
•
To define meaning of dimension in physics
•
To check equation validity using dimensional analysis
•
To define the international system of units SI
•
To convert units from one system to another .
•
To calculate order of magnitude
•
To account significant figures
Description of the Chapter
Terminology of the unit •
Standards :The term standard refers to the physical object on which the unit of
measurement is based
•
Significant figure : the number in which the last digit is uncertain or doubtful
•
Model : Imagining a model for a physical system that is related to the
phenomenon
•
Order of magnitude : to express an estimation as a power of 10 ( fo𝑟 𝑒𝑥𝑎𝑚𝑝𝑙𝑒 103
, …. )
•
Dimension :A dimension is a measure of a physical variable (without numerical
values) {For example, length is a dimension, but it is measured in units of feet (ft)
or meters (m).
Learning resources of
the unit
Textbook , internet
Number of lessons in
the unit
6 lessons
Table of Content
▪
1.1 standards of Length, Mass and Time
▪
1.2 Matter and Model Building
▪
1.3-Dimensional Analysis
▪
1.4 Conversion of Units
▪
1.5 Estimates and Order -of- Magnitude Calculations
▪
1.6 Significant Figures
1.1 STANDARDS OF LENGTH, MASS AND TIME
What is physics ?
physics, science that deals with the structure of matter and the
interactions between the fundamental constituents of the
observable universe.
Such as
:
the behaviour of objects under the action of given forces
the nature and origin of gravitational, electromagnetic, and nuclear
force fields
Build models of physical phenomena ….
Ultimate Goal OF PHYSICS IS the formulation of a
few comprehensive principles that bring together
and explain all natural phenomena.
1.1 STANDARDS OF LENGTH, MASS AND TIME
Standards are: the fundamental reference for a system of weights and
measures, against which all other measuring devices are compared
( calibrated )
standards used for measurements must not change with time
kilogram
Physics like all sciences are based on measurements and comparisons.
Thus, we
need rules about how things are measured and compared, and we need
experiments to establish the units for those measurements and comparisons
Standards of length, mass and time
meter
the distance
travelled by
light in vacuum
during
a time of
(1/299 792 458)
second.
kilogram
the mass of a specific
platinum–iridium alloy cylinder
kept at the International Bureau
of Weights
and Measures at Sèvres, France
second
9 192 631 770 times the period of
vibration of radiation from the
cesium-133 atom
1.1 STANDARDS OF LENGTH, MASS AND TIME
Dimension and unit
In physics, the word dimension denotes the physical nature of a quantity
Same physical quantity can be expressed in different units, for example the
distance between two points, can be measured in feet, meter, centimetre ,
kilometre ….
There is a difference between dimensions and units. A dimension is a
measure of a physical variable (without numerical values), while a unit is
a way to assign a number or measurement to that dimension.
Primary( basic )
Dimension
Symbol
SI unit
C.G.S unit
English unit
mass
M
kg (kilogram)
g ( gram )
lb (pound-mass)
length
L
m (meter)
cm ( centimetre )
ft (foot)
time
T
s (second)
s (second)
s (second)
▪ 1.2 Matter and Model Building
▪
1.3-Dimensional Analysis
Physical quantities can be classified as :
Basic ( primary )
mass, length, time
temperature, electric
current, amount of light,
and amount of matter
derived
Such as :
Force , power , work
, acceleration ,
velocity ,…..
Primary (sometimes called basic) dimensions are defined as independent or fundamental
dimensions, from which other dimensions can be obtained.
Example :
What are the dimension and unit
of :
❑ Velocity
❑ Acceleration
❑ Force
Example
( P9-page 15 – Textbook)
Example
( P14 -page 16 –
Textbook)
Dimensional analysis
Can be used
to
Find
dimension
and unit of a
physical
quantity
Example :
What are the dimension and
unit of :
❑ Velocity
❑ Acceleration
❑ Force
Check the
consistency of
equation
According to the dimensional analysis rules,
is the relation F = mvr-1, where unit of F is
kg.m.s-2, unit of m is kg , unit of v is m.s-1, and
that of r is m, is correct ( True) or not correct
(False)?
Find
unknowns
Use dimensional analysis to determine the
unknowns n, m, in the correct relation
S = A BnCm ,where A is dimensionless
constant, the unit of S is meter, the unit of
B is m .sec-2, unit of C is sec
TRY THE
FOLLOWING
According to the dimensional analysis rules,
is the relation F = mvr-2, where unit of F is
kg.m.s-2, unit of m is kg , unit of v is m.s-1, and
that of r is m, is correct ( True) or not correct
(False)?
Use dimensional analysis to determine the
magnitudes of unknowns a, b, and c in the correct
relation T=A Pa Db Ec where A is dimensionless
constant , the unit of T is second, the unit of P is kg
.m-1.sec-2, unit of D is kg.m-3 and unit of E is
kg.m2.sec-2.
1.4 Conversion of Units
Primary( basic )
Dimension
Symbol
SI unit
C.G.S unit
English unit
mass
M
kg (kilogram)
g ( gram )
lb (pound-mass)
length
L
m (meter)
cm ( centimetre )
ft (foot)
time
T
s (second)
s (second)
s (second)
Some times we have to convert unit from one system to another …
conversion can be simple ( direct) or we have to use chain conversion
…some examples are listed below
Example 1.3 – page 10
P 16, page 16 ( textbook)
Example 1.3 – page 10
Example 1.3 Is He Speeding?
On an interstate highway in a rural region of
Wyoming, a car is traveling at a speed of 38.0
m/s. Is the driver exceeding
the speed limit of 75.0 mi/h?
Extra example 10
Convert а 2.27 𝑓𝑡 2 tо units оf 𝑚2
. (1.00 m = 3.28 ft)
Rules to identify significant figures
1- All non- zero digits and any zero
contained between non-zero are
significant figures
143
25087
12.076
3 significant figures
5 significant figures
5 significant figures
2- Zeros may or may not be significant
figures
a)
Those used to position the decimal point in such
numbers as 0.03 and 0.0075 are not significant.
Thus : 0.03 -------- 1 significant figures
: 0.0075 ---- 2 significant figures
b)
When the zeros come after other digits, however, there is
the possibility of misinterpretation
To overcome this misinterpretation, we can express the
number in scientific notation to indicate the number of
significant figures:
For example : if the mass of an object is given as 1500 g
This value can be express in different ways according to
the number of significant figures in the measured values
1500 𝑔 = 1.5𝑥103 2 significant figures
1500 𝑔 = 1.50𝑥103 3 significant figures
1500 𝑔 = 1.500𝑥103 4 significant figures
Summary
❑ Rule
Example
❑ Any none zero number is always
significant
237
3 sig. fig
❑ Any zero between non zero numbers is
significant
46098
5 sig. fig
❑ Any zero before a non zero numbers is
NOT significant ( Leading zero )
0.00984
3 sig. fig
❑ Any zero after a non zero numbers is
1200
significant ONLY IF there is a decimal in
the number ( Trailing zero )
120.0
2 sig. fig
❑ Exact numbers have infinite amount of
significant figures
( physical constants and units … )
Infinite
number of
sig. fig.
1 inch =
2.54 cm
4 sig. fig
Rules for significant figures in
mathematical operations
Multiplication and division :
When multiplying ( or dividing )
several quantities, the number of
significant figures in the final
answer is the same as the
number of significant figures in
the quantity having the smallest
number of significant figures .
Examples :
1) 3.22 x 2.1 = 6.762 =6.8
3 sig. figs.
2 sig. figs.
2 sig. figs.
For any measured value , it can be
written as ( considering its
uncertainty )
(A± ΔA), for example :
Width of a rectangle is
2.4 ± 0.1 cm
In this case the uncertainty is 0.1cm
and the fractional ( relative)
0.1
uncertainty is ( ) = 0.04
2.4
For calculated values ( volume of a sphere , disc area ,
cylinder volume and so on … ) we can use
differentiation to get fractional uncertainty :
For example if you have a solid sphere of radius ( r ± Δr )
then its volume fractional uncertainty can be derived
as :
4
𝑉 = 3π 𝑟 3
Now
𝑑𝑉
= 4 π 𝑟2
𝑑𝑟
dV = 4 π 𝑟 2 𝑑𝑟
Divided both side by ( Volume )
2) 24 x 3.28 = 78.72 = 79
dV 4 π 𝑟 2 𝑑𝑟
= 4 3
𝑉
π𝑟
3
2 sig. figs.
3 sig. figs.
2 sig. figs.
dV
𝑉
=3(
𝑑𝑟
)
𝑟
See problem
52 solution