Transcript Slide 1

Do you hear me? I am a foreigner ! Use it !
If you don’t understand something, blame it on me!
There will be times (
) that you don’t have a clue what
I am talking about.
Know that probably 90% of the class doesn’t understand it either.
I didn’t understand it at your age.
Be the brave one (smart too) who is going to ask.
And don’t start with: “This is probably a dumb question ….”
In order to ask a “smart” question, you already have to know what
you want to ask about. It is impossible. Like a cat catching her tail.
You are going to school to learn. I know that.
Do you ?
It's not that I'm so smart,
it's just that I stay with problems longer.
WHAT IS PHYSICS?
The study of matter, energy, and
the interactions between them
… in other words, everything!
“Physics investigates the essential nature of the
world, and biology describes a local bump.
Psychology … describes a bump on a bump.”
Willard Van Orman Quine,
American philosopher (1908 – 2000)
All physical phenomena in our world are more or less successfully
described in terms of one or more of the following theories:

Classical Mechanics – matter, motion, forces, and energy.
Only describes objects bigger than atoms and slower than light.

Thermodynamics – heat and temperature

Electromagnetism – electricity, magnetism, and light

Relativity – particles moving at any speed, including very
high speeds (close to the speed of light)

Quantum Mechanics – behavior of submicroscopic particles
Side Note



Theory of Classical Mechanics (Newton) worked perfectly for more than
100 years – and still works in most circumstances today.
Limitation: it cannot successfully describe fast moving small particles.
Leaders of Modern physics (Einstein, Planck, Heisenberg, Bohr, etc.) had
to be open-minded when data didn’t fit with established theories
“No amount of experimentation can ever prove me
right; a single experiment can prove me wrong”
-- Albert Einstein
● Special theory of relativity – Albert Einstein.
In nearly all everyday situations, Einstein’s theory gives
predictions almost the same as Newton’s.
Main distinction is in extreme case of very high speed
(close to the speed of light)
The new theory gave us much more: Our view of the world is affected with that theory.
– Our concepts of space and time underwent a huge change
– mass and energy as a single entity ( E = mc2 ).
Class structure
Major Objectives



Understand physical phenomena not just equation hunt
Build problem-solving abilities
Communicate scientific knowledge simply and precisely
using math, graphs, pictures, and words
Assessment



Daily work
Labs & Projects
Major Quizzes and Exams
20%
20%
60%
No work
or
unintelligible work
= no credit!
Class structure
Rules




Respect each other’s time and learning
Bring calculator every day!
NO computers or phones (unless I specify)
Non-distracting food / drink is ok
Keys to success

Practice, Practice, Practice!
 Get help early & often … then try again on your own
 DON’T GIVE UP … studies say the single most important
factor in success at any task is GRIT
INTRODUCTION
The goal of physics is to gain deeper understanding of the
world in which we live.
Physics is the study of the fundamental laws of nature.
Remarkably, we have found that these laws can be expressed
in terms of mathematical equations. As a result, it is possible to
make precise, quantitative comparisons between the
predictions of the theory-derived from the mathematical form of
the laws – and the observations of experiments.
http://www.winbeam.com/~trebor/prelude.html
Robert J. Sciamanda, Edinboro University of Pennsylvania
No physicist or engineer ever solves a real problem. Instead she/he
creates a model of the real problem and solves this model problem.
This model must satisfy two requirements: it must be simple enough
to be solvable, and it must be realistic enough to be useful.
The theories and "laws" of physics are also models. Whether in the
solving of a particular engineering problem or in the search for the
wide ranging laws of physics, the art of scientific analysis consists in
the creation of useful models of reality. The model is the interface
between reality and the human mind. When we try to explain a new
phenomenon we reach for something familiar.
For example Rutherford's atomic model resembles the planetary motion in
solar system. Therefore, Rutherford's model of an atom is called planetary
model.
Examples:
We know everything about the motion if we know the
position and the velocity of that object at any time.
Motion of an object can be very complicated
Question: Do all points on the ball follow the same path
at the same time?
Is head at the same position as the wheels?
Do legs follow the same path as the head?
The simplest model: we choose to ignore everything
that is not important (color) or too complicated (shape,
size, spin, air resistance)
Look at the center of mass of the hammer.
The path is very simple: parabola
click me
Simplifying complicated situations: the system we are
going to study will be treated as POINT OBJECTS
– so shape, no size, no spin, no relative motion of the body parts
Point Object: - imagine the center of mass of the car or hammer and
imagine that we squished the car or hammer so that the whole mass
is concentrated at that point
– we draw the whole object it as a small circle
we call it: a point object (surprise).
Unit 1: Vectors and Math skills
Statement of Inquiry:
Math is a tool for explaining physical phenomenon
AOI: Human Ingenuity
Todays Objectives:





Define physics and describe the types of phenomena studied by
each branch of physics
Differentiate between scientific theories, laws, and hypotheses
Dimensional analysis
Express numbers in scientific notation
Recognize SI prefixes
The nature of science – Scientific theories
Scientific ideas are developed by making and testing predictions. Nothing is
ever proven in science, tests can merely support or disprove an idea.
… but some ideas have more support than others
Hypothesis – educated guess
tentative and testable statements that must be capable of
being supported or not supported by observational evidence
Theory – one (or several related) hypotheses that have been tested
(sometimes mathematically only) and supported many many times
by multiple independent researchers;
usually explain why something happens
Law
– finding proves to be true for long periods of time – generalizes
a body of observations with no known exceptions; only describes
events does NOT explain why
Example:
Hypotheses come and go by the thousands, but theories often
Newton’s
Gravitation
is an equation
that or
generalizes
remain toLaw
be of
tested
and modified
for decades
centuries.force
of attraction between 2 or more objects.
Einstein’s Theory of Relativity is a (well supported) idea about why
masses exert forces on other masses
Hypothesis or Theory or Law?
● The universe began almost 14 billion years ago with
a massive expansion event.
Theory
● Male pupfish have bright colors to attract mates
● Animals change over time
hypothesis
Law of Evolution
●Traits that confer a reproductive advantage tend to increase
in a population over time
Theory of Natural Selection
Why do we use Scientific Notation?
The mass of the Earth is
5972000000000000000000000000 kg
Is this a reasonable way to express this number?
Of course not!
Much better way:
5.972 X 1027 kg
This is known as
scientific notation
Swine flu virus: diameter of 10 to 300 nanometers
(nanometer is equal to one billionth of a meter)
0.0000000000001m becomes 1.0 x 10-13m
Elegance in physics:
We use Scientific Notation or Prefixes when dealing with numbers
that are very small or very big.
Examples:
1.
The best current estimate of the age of the universe is
13 700 000 000 = 1.37 × 1010 years = 13.7 billion years
scientific
notation
prefix
2. electron mass = 0.000 000 000 000 000 000 000 000 000 000 91 kg
= 9.1 × 10-31 kilograms
3. 0.00354 m = 3.54 x 10-3 m = 3.54 mm
Scientific Notation
Practice individually. If you have time, check with table
partner. You have 3 minutes.
=
3.004 X 10-5
0.00003004
= 4.56 X 10-2
2) 0.0456
= 1.045004 X 106
3) 1045004
= 9.340 X 103
4) 9340
= 0.0010053
5) 1.0053 X 10-3 (standard notation!)
6) 5.302 X 104
(standard notation!) = 53020000
1)
more
practice
Another reason to use Scientific Notation?
Scientific notation is useful
1) For very large or small numbers
2) For showing the precision of a measurement
How else might we
handle very small
or large numbers?
SI prefixes!
Example:
If I say a pumpkin is 200 lb, what do I really mean?
Maybe I mean that it is exactly 200 lbs (closer to 200 lbs than
to 201 or 199 lbs).
But, maybe I mean that is only roughly 200 lbs (closer to 200
lbs than 300 or 100 lbs)
If I say that a pumpkin is 2.00 X 102 lbs, the precision is clear … it
is between 201 and 199. More on this, later!
Prefixes:
SI UNIT CONVERSIONS
Which is bigger
a mm or a Mm?
a ng or a g?
Mm
g
base unit
femto
f
pico
nano
p
n
m
10-15
10-12
10-9
10-6
Smaller units
micro
mili
1
m
10-3
100
centi
deci
c
10-2
d
10-1
kilo
mega
giga
tera
k
M
G
T
103
106
109
1012
Larger units
every step is 10± 1 power
They are grouped into steps 10± 3
NEXT: Unit conversions involving SI unit prefixes
f
p
n
m
10-15
10-12
10-9
10-6
m
10-3
c
10-2
100
d
10-1
k
M
G
T
103
106
109
1012
smaller unit →
bigger number
larger unit →
smaller number
5 𝑚ℓ = _______ 𝑘ℓ
1
5 𝑘𝑚 = _______ 𝑐𝑚
=1
=1
1𝑘ℓ
5 𝑚ℓ = 5 𝑚ℓ ×
= 5 × 10−6 𝑘ℓ
6
10 𝑚ℓ
105 𝑐𝑚
5 𝑘𝑚 = 5𝑘𝑚 ×
= 5 × 105 𝑐𝑚
1𝑘𝑚
* Note: The larger unit has a 1 in the conversion factor (i.e. 1 kℓ and 1 km). Easier !
or
−6
1 𝑚ℓ = 10 𝑘ℓ
5𝑚ℓ = 5 × 10−6 𝑘ℓ
or
1𝑘𝑚 = 105 𝑐𝑚
5𝑘𝑚 = 5 × 105 𝑐𝑚
The wavelenagth of green light is 500 nm. How many meters is this?
500 𝑛𝑚 ×
or
1𝑚
−9 𝑚 = 5 × 10−7 𝑚
=
500
×
10
109 𝑛𝑚
1 𝑛𝑚 =
start: nm
end: m larger unit is “m”
“1m” in numerator
10−9 𝑚
500 𝑛𝑚 = 500 × 10−9 𝑚 = 5 × 10−7 𝑚
Practice individually. You have 5 minutes.
I have 906 gigabyte hard drive on my computer. How many bytes of data will it hold?
906 𝐺𝑏𝑦𝑡𝑒𝑠 = 906 × 1012 𝑏𝑦𝑡𝑒𝑠 = 9.06 × 1010 𝑏𝑦𝑡𝑒𝑠
How many liters is 16 𝜇ℓ ?
4.3 x 104 ns = ? µs
5.2 x 108 ms = ? ks
16 𝜇ℓ = 1.6 × 10−5 ℓ
1 𝑛𝑠 = 10−3 𝜇𝑠
4.3× 104 𝑛𝑠 = 43 µs
1 ms = 10-6 ks
5.2 × 108 𝑚𝑠 = 520 𝑘𝑠
A dime is 1.0 mm thick.
A quarter is 2.5 cm in diameter.
The average height of an adult man is 1.8 m.
Diameter of atomic nucleus ≈ 5 fm
Diameter of the atom ≈ 100 pm =100 000 fm
If an atom were as big as a football field nucleus would be about the size of a pea in the centre.
Conclusion: you and I and all matter consists of almost entirely empty space.
Diameter of a red blood cell ≈ 8 μm
Diameter of Earth ≈ 13 Mm
Diameter of sun ≈ 1.4 Gm
Diameter of Milky Way ≈ 9500 Tm
visible universe is thought to be around
1025
m
Scale of the Universe
http://htwins.net/
Anything you measure or calculate in physics
Physical quantities are expressed in UNITS
Time, length, and weight are all separate dimensions
 You can only convert between measurements within the same
dimension
For example:
 Time can be measured in seconds, minutes, or hours
 You CAN convert seconds  minutes  hours
 You CANNOT convert seconds  centimeters

In short : Nature of the beast (physical quantity) is dimension (quality).
To express the quantity of the beast we need units.
SI Units
The International System of Units (abbreviated SI from French: Système
international d'unités) is the modern form of the metric system adopted in 1960.
Why use SI units?
● universal
● easy (metric system)
Dimensions aren't the same as units. For example, the physical quantity,
speed, may be measured in units of meters per second, miles per hour etc.;
but regardless of the units used, speed is always a length divided a time, so
we say that the dimensions of speed are length divided by time, or simply L/T.
Similarly, the dimensions of area are L2 since area can always be calculated as
a length times a length.
Confusing?????
Dimension of physical quantity distance is length.
Dimension of speed is length/time
ALL physical dimensions can be expressed in terms of combinations of
seven basic /fundamental dimensions. These seven dimensions have been
chosen as being basic because they can be measured directly and easily.
Derived dimensions are combinations of 7 basic ones.
Basic
Physical
Quantity
Basic
Dimension
Basic
SI Unit
Distance,
height,width
Length (L)
meter
(m)
Mass (m)
Mass (M)
kilogram
(kg)
Time (t)
Time (T)
second
(s)
Electric
Current (I)
Electric
Current (I)
ampere
(A)
Temperature
Temperature
kelvin (K)
Amount of
matter
Amount of
matter
mole
Intensity of
light
Intensity of
light
candela
(cd)
Derived
Physical
Quantity
Derived
Dimension
Derived
SI Unit
area
L2
m2
volume
L3
m3
speed
L/T
m/s
acceleration
L/T2
m/s2
ML/T2
kg.m/s2
newton (N)
force
power
mass density
M L2/T3
M/
L3
kg.m2/s3
watt (W)
kg/m3
Which one of the following quantities are
dimensionless (and therefore unitless)?
1. 68°
dimensionless
2. sin 68°
dimensionless
3. e
dimensionless
4. force
not dimensionless
5. 6
dimensionless
6. frequency
not dimensionless
7. log 0.0034
dimensionless
In the study of mechanics, we shall be concerned with physical quantities/dimensions
(and units) that can be described in terms of three dimensions:
length (L), time (T) , and mass (M).
The corresponding basic SI- units are:
Length – 1 meter (1m) is the distance traveled by the light in a vacuum during
a time of 1/299,792,458 second.
Mass – 1 kilogram (1 kg) is defined as a mass of a specific platinum-iridium
alloy cylinder kept at the International Bureau of
Weights and Measures at Sevres, France
Time – 1 second (1s) is defined as 9,192,631,770 times the period of one
oscillation of radiation from the cesium atom.
kilogram is the only SI unit with a prefix as part
of its name and symbol.
Determine the dimensions and corresponding SI units of the following quantities:
1.
volume
L3,
m3
2.
acceleration (velocity/time)
L/T2,
m/s2
3.
density (mass/volume)
M/L3,
kg/m3
4.
force (mass × acceleration)
M•L/T2,
kg•m/s2
5.
charge (current × time)
I•T,
A•s
6.
Height
L,
m
7.
pressure (force/area)
M/(L•T2),
kg/(m•s2)
8.
work (force × distance)
M•L2/T2,
kg•m2/s2
½ is number, it cannot be measured → no unit
Determine if the following equations are dimensionally correct.
1. x = xo + vo t + (1/2) a t2
where x is the displacement at time t, xo is the displacement at time t = 0,
vo is the velocity at time t = 0, a is the constant acceleration
𝐿=𝐿+
𝐿
𝐿
𝑇 + 2 𝑇2
𝑇
𝑇
Practice time
1𝑚3 = 1(102 𝑐𝑚)3 = 106 𝑐𝑚3
1𝑚3 = 1(103 𝑚𝑚)3 = 109 𝑚𝑚3
1𝑐𝑚3 = 1(10−2 𝑚)3 = 10−6 𝑚3
1𝑚𝑚3 = 1(10−3 𝑚)3 = 10−9 𝑚3
Take couple of minutes to practice.
Which of the following most accurately describes the velocity of this
boulder the instant before hitting the ground. The acceleration due to
gravity is g.
A) (gh)1/2
B) 2gh
C) (2gh)1/2
D) mgh
1/2
𝐿
𝐿
𝐿
=
𝑇2
𝑇
𝐿
𝐿2
𝐿= 2
𝑇2
𝑇
𝐿
𝐿
𝑇2
1/2
=
𝐿
𝑇
𝐿
𝐿2
𝑀 2𝐿 = 𝑀 2
𝑇
𝑇
we don’t know without further information
both A) and C) are dimensionaly correct
7.2 m3 → mm3
100
mm3
→
m3
75 g/cm2 → kg/m2
7.2 𝑚3 = 7.2 103 𝑚𝑚 3 = 7.2 x 109 𝑚𝑚3
100 𝑚𝑚3 = 100 10−3 𝑚
𝑔
75 2
𝑐𝑚
𝑚
𝑠
= 75
20 m/s → km/h
20
72 km/h → m/s
𝑘𝑚
72
ℎ
60 mi/h = ? m/s
1 mi = 1609 m
= 20
𝑚𝑖
60
ℎ
10−3 𝑘𝑔
10−2 𝑚 2
10−3 𝑘𝑚
1
3600 ℎ
= 72
=
103 𝑚
3600 𝑠
𝑘𝑚
96
ℎ
3
= 10−7 𝑚3
= 750 kg/m2
= 72 km/h
= 20 m/s
103 𝑚
3600 𝑠
= 27 m/s
Uncertainty and error in measurement
No measurement can be "exact". You can never, NEVER get exact
value experimentally
The inevitable uncertainty is inherent in measurements.
It is not to be confused with a mistake or blunder
Accuracy is the closeness of agreement between a measured value
and a true or accepted value
Precision is the degree of exactness
(or refinement) of a measurement (results from
limitations of measuring device used).
Think of it while you are playing darts, like this:
precise, not
accurate, not neither precise,
both accurate
accurate
precise
nor accurate
and precise
Precision is really about detail. It has nothing to do with accuracy.
Accuracy is about giving true readings, not detailed readings.
There are 2 types of errors in measured data:
random and systematic.
It is important to understand which you are dealing with,
and how to handle them:

Random: refer to random fluctuations in the measured data due to:
● the readability of the instrument
● the effects of something changing in the surroundings between measurements
● the observer being less than perfect J
● Random errors can be reduced by averaging.
A precise experiment has small random error.
 Systematic: (measurements that are either consistently too
large, or too small) can result from:
● poor technique (e.g. carelessness with parallax)
The observer being less than perfect in
the same way during each measurement. - J
● zero error of an instrument (e.g. a ruler that has been shortened
by wear at the zero end, or a scale that reads a value when
nothing is on it); Instrument does not read zero when it should
– to correct for this, the value should be subtracted from every reading)
● an instrument being wrongly calibrated (e.g. every time measurement
is measured too large).
● can be detected using different methods of measurement.
• No measurement can be "exact". This would require a
measuring instrument with marks infinitely close together –
which is clearly impossible.
When certain quantities are measured, the measured values
are known only to within the limits of the experimental
uncertainty (depending on the quality of the apparatus, the
skill of experimenter, ...).
SIGNIFICANT FIGURES are reliably known digits
+ one uncertain (estimate)
Reading: 52.8 mℓ
52 mℓ – reliably known
0.8 mℓ is uncertain – estimate
☞
All digits 1,2,3…9 count as significant digits.
7 642.95 (6 SF)
About Zeros:
☞
Zeros between other non zero digits are significant.
50.3 (3 SF ), 3.0025 (5 SF)
☞
Zeros in front of non zero digits are NOT significant:
0.67 (2 SF), 00843 ( 3 SF), 0.0008 (1 SF).
Zeros at the beginning merely locate the decimal point.
☞
Zeros to the right of a decimal are significant.
57.00 (4 SF), 2.000 000 (7 SF)
Zeros at the end of a DECIMAL number are significant
(it means: we know that digit is 0)
☞
Zeros at the end of a number are ambiguous.
34 000 m3 (2, or 3 or 4 or 5 SF?).
☞
Rule: use scientific notation if you know how many
significant figures there are
for example if this is the result of calculations, and you
know
there are only 2 SF, then the result is:
34 000 m3 = 34 x 103 m3
Significant digits in a calculation:
(DON’T ROUND UTILL THE END OF CALCULATIONS)
Addition or subtraction:
The final answer should have the same number of DECIMALS as the
measurement with the smallest number of decimals.
2.2 + 1.25 + 23.894 = 27.164 → 27.2
2.2??
1.25?
23.894
27.164 → 27.2
you don’t know second decimal in the first measurement
and third decimal in second measurement, so the result
can not have reliably known second and third decimal.
97.329 - 47.54 = (49.789) = 49.80
(3 dec) - (2 dec)
= (2 dec)
Answer should be reported with 2 dec only
Multiplication, Division, Powers and Roots:
The final answer should have the same number of SIGNIFICANT DIGITS
as the measurement with the smallest number of significant digits
Ex:
121.30 x 5.35 = (648.955) = 649
(5 SF) x (3 SF) =
= (3 SF)
Answer should be rounded up to 3 SF only