Second Stage
Geology Dept.
2014-2015
Alan Othman Saeed
LEARNING GOALS
By studying this chapter, you will learn:
• Three fundamental quantities of physics and the units physicists use to
measure them.
• The difference between scalars and vectors, and how to add and subtract
vectors graphically.
• What the components of a vector are, and how to use them in calculations.
• What unit vectors are, and how to use them with components to describe
vectors.
• Scalar product of vectors.
Overview: What is Physics?
(1) Physics seeks to describe observations in terms of quantified
measurements.
(2) Physics seeks to discover relationships between different measurements
and to express the relationships in terms of "physical laws" (i.e.
mathematical statements).
Example: F=ma (force = mass x acceleration)
(3) Physics seeks to discover the nature of forces (force laws). Forces arise
from interactions between two objects. At present, there are four known
fundamental interactions
(forces): gravitational, electromagnetic, strong nuclear, and weak nuclear
interactions.
(4) Physics seeks to formulate models and theories (i.e. conceptual
frameworks) which unify the physical laws.
atomic model = nucleus + electrons (model: quantum theory)
Standards and Units
physics is an experimental science
• Experiments require measurements, and we generally use numbers to describe
the results of measurements.
• Any number that is used to describe a physical phenomenon quantitatively is
called a physical quantity.
• Basic quantities: Some physical quantities are so fundamental that we can
define them only by describing how to measure them.
• derived quantities they can be expressed as combinations of a small number
of basic quantities.
In mechanics, the three basic quantities are length, mass, and time.
All other quantities in mechanics can be expressed in terms of these three.
•
Two examples are measuring a distance by using a ruler and measuring a
time interval by using a stopwatch. In other cases we define a physical
quantity by describing how to calculate it from other quantities that we
can measure.
• Thus we might define the average speed of a moving object as the
distance traveled (measured with a ruler) divided by the time of travel
(measured with a stopwatch).
• quantity = Number
meaningless
• Physical quantity = Number + Unit .
Meaningful
• When we measure a quantity, we always compare it with some reference
standard. Such a standard defines a unit of the quantity.
In 1960, an international committee established a set of standards for the
fundamental quantities of science. It is called the metric system or the
SI (Systèm International) units:
Length……….(the Meter)
Mass ………………..(the Kilogram)
Time………………………..(the Second)
Other SI standards established by the committee are those for
Temperature ………..(the Kelvin)
Electric current…………..(the Ampere)
Luminous intensity……………(the Candela)
The amount of substance………..(the Mole)
• Length: The SI unit of length, the meter (m) was redefined as the distance
traveled by light in vacuum during a time of 1/299 792 458 second
(October 1983)
• Mass: The SI unit of mass, the kilogram (kg), is defined as the mass of a
specific platinum–iridium alloy cylinder kept at the International Bureau of
Weights and Measures at Sèvres, France. (1887)
• Time: The SI unit of time, The second (s) is now defined as 9 192 631 770
times the period of vibration of radiation from the cesium atom. (1967)
1 second = 9,192, 631,770 cycles of the standard Cs-133 transition
Since Einstein’s discovery of the linkage between space and time, precise
measurement of time intervals requires that we know both the state of
motion of the clock used to measure the interval and, in some cases, the
location of the clock as well.
• latest definition establishes that the speed of light in vacuum is precisely
299 792 458 meters per second.
• Unit Prefixes
In addition to the basic SI units of meter, kilogram, and second, we can also
use other units, such as millimeters and nanoseconds, where the prefixes
milli- and nano denote multipliers of the basic units based on various powers
of ten.
Dimensional analysis
Balancing units on both sides of an equation is called dimensional analysis.
Example:
Distance travelled = speed x time
D =v t
m = (m/s) s
** Both sides of an equation must have the same unit (in this case, it is meter),
if they don’t then your equation is incorrect.
Matter and Model Building
If physicists cannot interact with some phenomenon directly, they often
imagine a model for a physical system that is related to the phenomenon.
In this context, a model is a system of physical components, such as electrons
and protons in an atom.
Once we have identified the physical components, we make predictions
about the behavior of the system, based on the interactions among the
components of the system and/or the interaction between the system and
the environment outside the system.
• If you have a 1-kg cube of solid gold
• Is this cube nothing but wall-to-wall gold, with no empty space?
• If the cube is cut in half, the two pieces still retain their chemical identity
as solid gold.
• But what if the pieces are cut again and again, indefinitely? Will the
smaller and smaller pieces always be gold?
The Greek model atomos means “not sliceable.”
1911 (nucleus)
1897 (electron)
that lead to others questions ???
Does the nucleus have structure?
That is, is the nucleus a single particle or a collection of particles?
early 1930s (protons and neutrons)
• The proton carries a positive electric charge, and a specific chemical element is
identified by the number of protons in its nucleus. This number is called the
atomic number of the element.
• In addition to atomic number, there is a second number characterizing atoms—
mass number, defined as the number of protons plus neutrons in a nucleus.
The atomic number of an element never varies (i.e., the number of protons does
not vary) but the mass number can vary (i.e., the number of neutrons varies).
• A neutron has no charge and a mass that is about equal to that of a
proton. One of its primary purposes is to act as a “glue” that holds the
nucleus together.
• But is this where the process of breaking down stops?
• six different varieties of particles called quarks, which have been given the
names of up, down, strange, charmed, bottom, and top.
• The up, charmed, and top quarks have electric charges of +2/3 that of the
proton.
• the down, strange, and bottom quarks have charges of -1/3 that of the
proton.
A proton, composed of two up quarks (2/3) and one down quark (-1/3).
Proton is +1
A neutron, composed of two down quarks (-1/3) and one up quark (2/3).
Neutrons are 0 (a net charge of zero)
historical models of the structure of matter
• This process of building models is one that you should develop as you
study physics. You will be challenged with many mathematical problems to
solve in this study.
• One of the most important techniques is to build a model for the
problem— identify a system of physical components for the problem, and
make predictions of the behavior of the system based on the interactions
among the components of the system and/or the interaction between the
system and its surrounding environment.
Coordinate Systems
Many aspects of physics involve a description of a location in space.
• Cartesian coordinates (rectangular coordinates): (x, y)
• The plane polar coordinates (r, θ) of a point are represented by the
distance r and the angle θ, where θ is measured counterclockwise from
the positive x axis.
Conversion between Cartesian and polar coordinates
These four expressions relating the coordinates (x, y) to the coordinates (r, θ) apply
when positive θ is an angle measured counterclockwise from the positive x axis.
EX: The Cartesian coordinates of a point in the xy plane are (x, y) =
(- 3.50, - 2.50) m, as shown in the Figure. Find the polar coordinates of this
point.
Solution
Vector and Scalar Quantities
• A scalar quantity is completely specified by a single value with an
appropriate unit and has no direction.
• Examples of scalar quantities are volume, mass, speed, temperature and
time intervals.
• The rules of ordinary arithmetic are used to manipulate scalar quantities.
• A vector quantity is completely specified by a number and appropriate
units plus a direction.
• Examples of scalar quantities are velocity and force
• vectors requires a different set of operations.
Vectors are represented graphically by arrows. An arrow used to represent a vector has
a length proportional to the vector’s magnitude (e.g., the larger the magnitude, the
longer the length of the vector) and points in the same direction as the vector.
Some Properties of Vectors
Equality of Two Vectors:
Adding Vectors (graphical methods):
This shows that the order of terms in a vector
sum doesn’t matter. In other words, vector
addition obeys the commutative law.
CAUTION
Magnitudes in vector addition: It’s a common error to conclude that if
C = A+B then the magnitude C should equal the magnitude A plus the
magnitude B. In general, this conclusion is wrong; for the vectors shown in
Figures above, you can see that C ˂ A+B. The magnitude of A+B depends on
the magnitudes of A and B and on the angle between A and B.
Only in the special case in which A and B are parallel is the magnitude of
C = A+B equal to the sum of the magnitudes of A and B .When the vectors are
antiparallel, the magnitude of C equals the difference of the magnitudes of A
and B. Be careful about distinguishing between scalar and vector quantities,
and you’ll avoid making errors about the magnitude of a vector sum.
Subtracting Vectors:
To construct the vector difference A-B ,you can either place the tail of –B at
the head of A or place the two vectors A and B head to head.
Multiplying a Vector by a Scalar:
• (A) (+m) then the product mA is a vector that has the same direction as A
and magnitude mA.
• (A) (- m) then the product -mA is a vector that has the opposite direction
of A and (–m) magnitude of A.
Components of a Vector
Using components to calculate the vector sum (resultant) of two or
more vectors.
Unit Vectors
• A unit vector is a vector that has a magnitude of 1, with no units. Its only
purpose is to point—that is, to describe a direction in space.
R=A+B
Ex:
Solution:
R=A+B
Products of Vectors
• Scalar Product:
Note that A and B need not have the same units, as is the case with any
multiplication.
That mean:
A.B = B.A
The scalar product is a scalar quantity, not a vector,
and it may be positive, negative, or zero.
a) A.B = +
b) A.B = c) A.B = 0
Dot products of unit vectors
Ex: Find the scalar product of the two vectors A.B in the below Figure. The
magnitudes of the vectors are A=4 and B=5.
Soulation:
𝝋 = 𝟏𝟑𝟎° − 𝟓𝟑° = 𝟕𝟕°
Second way:
Both methods give the same result, as they should.
Ex: Find the angle between vector A and B.
Solution: