1 CHAPTER ONE
PRELIMINARIES
The word physics comes from the Greek word meaning ―nature‖. Today
physics is treated as the base for science and have various applications
for the ease of life. Physics deals with matter in relation to energy
and the accurate measurement of natural phen omenon . Thus physics is
inherently a science of measurement. The fundamentals of physics form
the basis for the study and the development of engineering and
technology.
Measurement consists of the comparison of an unknown quantity with a
known fixed quant ity. The quantity used as the standard of measurement
is called ‗unit‘. For example, a vegetable vendor weighs the vegetables
in terms of units like kilogram.
Learning Objectives : At the end of this chapter , you will be able to:
Explain physics . Describe how SI base units are defined.
Describe how derived units are created from base units.
Express quantities given in SI units using metric prefixes.
Describe the relationships among models, theories, and laws . Know
the units used to describe various physical quantities . Become
familiar with the prefixes used for larger and smaller quantities .
Master the use of unit conversion (dimensional analysis) in solving
problems . Understand the relationship between uncertainty and the
number of significant figures in a number.
1.1. Physical Quantities and Measurement
Self Diagnostic Test :
Why do we need measurement in physics and our day -to-day lives?
Give the names and abbreviations for the basic physical quantities and
their corresponding SI units.
What do you mean by a unit?
2
Definitions:
Physical quantity is a quantifiable or assignable property ascribed to a
particular phenomenon or body, for instance the length of a rod or the
mass of a body.
Measurement is the act of compari ng a physical quantity with a certain
standard .
Scientists can even make up a completely new physical quantity that has
not been known if necessary. However, there is a set of limited number
of physical quantities of fundamental importance from which all other
possible quantities c an be derived. Those quantities are called Basic
Physical Quantities , and obviously the other derivatives are called
Derived Physical Quantities.
1.1.1. Physical quantities
A. Basic Physical Quantities:
Basic quantities are the quantities which cannot be expressed in terms
of any other physical
quantity. Example: length, mass and time.
B. Derived Physical Quantities:
Derived quantities are quantities that can be expressed in terms of
fundamental quantities . Examples: area, volume, density.
Giving numerical values for physical quantities and equations for
physical principles allows us to understand nature much more deeply than
qualitative descriptions alone. To comprehend these vast ranges, we must
also have accepted units in which to express them. We shall find tha t
even in the potentially mundane discussion of meters, kilograms, and
seconds, a profound simplicity of nature appears: all physical
quantities can be expressed as combinations of onl y seven basic
physical quantities.
We define a physical quantity either by specifying how it is measured or
by stating how it is calculated from other measurements. For example, we
might define distance and time by specifying methods for measuring them,
such as using a meter stick and a stopwatch. Then, we could define
averag e speed by stating that it is calculated as the total distance
traveled divided by time of travel.
3
Measurements of physical quantities are expressed in terms of units ,
which are standardized values. For example, the length of a race, which
is a physical q uantity, can be expressed in units of meters (for
sprinters) or kilometers (for distance runners). Without standardized
units, it would be extremely difficult for scientists to express and
compare measured values in a meaningful way .
1.1.2. SI Units: Basic and Derived Units
SI unit is the abbreviation for International System of Units and is the
modern form of metric
systemfinallyagreeduponattheeleventhInternationalconferenceofweightsandmeasures,1960.
This system of units is now being adopted throughout th e world and will
remain the primary system of units of measurement. SI system possesses
features that make it logically superior to any other
system and it is built upon 7 basic quantities and the ir associated
units (see Table 1.1 ).
Table 1.1: Basic quantities and their SI u nits
Table 1.2: Derived quantities, t heir SI units and dimensions
1.1.3. Conversion of Units
Measurements of physical quantities are expressed in terms of units ,
which are standardized values. To convert a quantity from one unit to
another, multiply by conversions factors in such a
4 way that you cancel the units you want to get rid of and introduce the
units you want to end up with. Below is the table for commonly use d
unit conversions (see Table 1.3).
Table 1.3 : Unit conversion of basic q uantities
Examples : 1. Length 0.02in can be converted into SI unit in meters
using table 1.3 as follow:
Solution:
0.02in= 0.02 x0.0254 m = 0.000508m = 5.08 x10-4m = 0.503 mm or 508µm.
2. Honda Fit weighs about 2,500 lb. It is equivalent to 2500 x0.4536kg =
1134.0kg.
1.2. Uncertaint y in Measurement a nd Significant Digits
Measurements are always uncertain, but it was always hoped that by
designing a better and better experiment we can improve the uncertainty
without limits. It turned out not to be the case. No measurement of a
physical quantity can be entirely accurate. It is important to know,
therefore, just how much the measured value is likely to deviate from
the unknown, true, value of the quantity. The art of estimating these
deviations should probably be called uncertainty analysis, Activities
: 1. A common Ethiopian cities speed limit is 30km/hr. W hat is this
speed in miles per hours?
2. How many cubic meters are in 250,000 cubic centimeters?
3. The average body temperature of a house cat is 101.5oF. What is this
temperature in Celsiu s?
5 but for historical reasons is refer red to as error analysis. This
document contains brief discussions about how errors are reported, the
kinds of errors that can occur, how to estimate random errors, and how
to carry error estimates into calculated results.
Uncertainty gives the range of p ossible values of the measure and,
which covers the true value of the measure and. Thus uncertainty
characterizes the spread of measurement results. The interval of
possible values of measure and is commonly accompa nied with the
confidence level. Therefore , the uncertainty also indicates a doubt
about how well the result of the measurement presents the value of the
quantity being measured.
All measurements always have some uncertainty. We refer to the
uncertainty as the error in the measurement. Errors fall into two
categories:
1. Systematic Error - errors resulting from measuring devices being out
of calibration. Such measurements will be consistently too small or
too large. These errors can be eliminated by pre -calibrating
against a known, trusted standa rd.
2. Random Errors - errors resulting in the fluctuation of measurements
of the same quantity about the average. The measurements are equally
probable of being too large or too small. These errors generally
result from the fineness of scale division of a me asuring device.
Physics is a n empirical science associated with a lot of measurements
and calculations. These calculations involve measurements with
uncertainties a nd thus it is essential for science students
to learn how to analyze these uncertainties (e rrors) in any
calculation. Systematic errors are generally ―simple‖ to analyze but
random errors require a more careful analysis and thus it will be our
focus. There is a statistical method for calculating random
uncertainties in measurements.
The followin g general rules of thumb are often used to determine the
uncertainty in a single measurement when using a scale or digital
measuring device.
1. Uncertainty in a scale m easuring device is equal to the smallest
increment divided by 2.
Example: Meter Stick (scale device)
6
2. Uncertainty in a digital measuring d evice is equal to the smallest
increment.
Example: A reading from digital Balance (digital device) is 5.7513 kg,
therefore
When stating a measurement , the uncertainty should be stated explicitly
so that there is no question about it. However, if it is not stated
explicitly, an uncertainty is still implied. For example, if we measure
a lengt h of 5.7 cm with a meter stick, this implies that the length can
be anywhere in the range 5.65 cm ≤ L ≤ 5.75 cm. Thus, L =5 .7 cm
measured with a meter stick implies an uncertainty of 0.05 cm. A common
rule of thumb is to take one -half the unit of the last decimal place in
a measurement to obtain the uncertainty. In general, any measurement can
be stated in the following preferred form:
Measurement = xbest±
Where , xbest= best estimate of measurement , = uncertainty (error) in
measurement .
1.2.1. Significant digits
Whenever you make a measurement, the number of meaningful digits that
you write down implies the error in the measurement. For example if you
say that the length of an object is 0.428 m, you imply an uncertainty of
about 0.001 m. To record this measurement as either 0.4 or 0.42819667
would imply that you only know it to 0.1 m in the first case or to
0.00000001 m in the second. You should only report as many significant
figures as are consistent with the estimated error. The quantity 0.428 m
is said to have th ree significant digits, that is, three digits that
make sense in terms of the measurement. Notice that this has nothing to
do with the “number of decimal places”. The same measureme nt in
centimeters would be 42.8 cm and still be a three significant figure .
The accepted convention is that only one uncertain digit is to be
r...
