Bojana Trninić - Radja

The most important thing about me

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.

Class structureMajor Objectives

Understand physical phenomena not just equation hunt Build problem-solving abilities Communicate scientific knowledge simply and precisely

using math, graphs, pictures, and words

AssessmentDaily work 30%Labs & Projects 10%Major Quizzes and Exams 60%

No work or

unintelligible work = no credit!

And out of blue moon: please do not let me see you chew chewing gum in my classroom

Class structureRules

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 Be a fighter

Unit 1: Vectors and Math skillsStatement of Inquiry:

Math is a tool for explaining physical phenomenonAOI: 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 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.

INTRODUCTION

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.

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)

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

All physical phenomena in our world are more or less successfully described in terms of one or more of the following theories:

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

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)

● Special theory of relativity – Albert Einstein.

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 ).

http://www.winbeam.com/~trebor/prelude.html

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.

Robert J. Sciamanda, Edinboro University of Pennsylvania

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

Examples:

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

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

click me

– we draw the whole object it as a small circle we call it: a point object (surprise).

The nature of science – Scientific theoriesScientific 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

Theory

Law

– educated guess tentative and testable statements that must be capable of being supported or not supported by observational evidence

– 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

– 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:

Newton’s Law of Gravitation is an equation that generalizes 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

Hypotheses come and go by the thousands, but theories often remain to be tested and modified for decades or centuries.

Hypothesis or Theory or Law?

● The universe began almost 14 billion years ago with a massive expansion event.

● Male pupfish have bright colors to attract mates

● Animals change over time

●Traits that confer a reproductive advantage tend to increase in a population over time

●Two bodies of mass m1 and m2 attract each other with a force that is proportional to the product of their masses

hypothesis

Theory of Evolution

Theory

Theory of Natural Selection

The Law of Gravitation

The mass of the Earth is5972000000000000000000000000 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

Why do we use 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

3. 0.00354 m = 3.54 x 10-3 m = 3.54 mm

Elegance in physics:We use Scientific Notation or Prefixes when dealing with numbers that are very small or very big.

1. The best current estimate of the age of the universe is 13 700 000 000 = 1.37 × 1010 years = 13.7 billion years

Examples:

scientific prefix notation

2. electron mass = 0.000 000 000 000 000 000 000 000 000 000 91 kg = 9.1 × 10-31 kilograms

Scientific Notation

Practice individually. If you have time, check with tablepartner. You have 3 minutes.

1) 0.000030042) 0.0456 3) 10450044) 93405) 1.0053 X 10-3 (standard notation!)6) 5.302 X 104 (standard notation!)

= 3.004 X 10-5

= 4.56 X 10-2

= 1.045004 X 106

= 9.34 X 103

= 0.0010053= 53020

more practice

Another reason to use Scientific Notation?

Scientific notation is useful 1) For very large or small numbers2) For showing the precision of a measurement

Example: If I say a 4 years young kid is 20 kg, what do I really mean?Maybe I mean that it is exactly 20 kg (closer to 20 kg than to 21 or 19 kg; by the way what is “exactly” ). But, maybe I mean that is only roughly 20 kg (closer to 20

kg than 30 or 10 kg)

If I say that the 4 years young kid is 2.0 X 101 kg, the precision is clear … it is between 20.1 and 19.9. More on this, later!

How else might we handle very small or large numbers?

SI prefixes!

Prefixes: SI UNIT CONVERSIONS

Which is biggera mm or a Mm? a ng or a g?

Mmg

Smaller units

every step is 10± 1 powerThey are grouped into steps 10± 3

femto pico nano micro mili kilo mega giga tera f p n m m k M G T

base unit1

Larger units

10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012

centi deci c d 10-2 10-1

NEXT: Unit conversions involving SI unit prefixes

5𝑚ℓ=¿ℓlarger unit →

smaller number

5𝑚ℓ=5𝑚 ℓ×(1ℓ1ℓ )

¿5𝑚ℓ ×( 10−3𝑘 ℓ103𝑚 ℓ )

5𝑚ℓ¿5𝑚ℓ ×( 𝑘ℓ106𝑚 ℓ )

¿5×10−6𝑘 ℓ

¿5×10−6𝑘 ℓ

= 1

= 1

or

or

5𝑚ℓ=5𝑚 ℓ×(10−3 ℓ1𝑚ℓ )( 1𝑘 ℓ

103 ℓ )=¿ 5×10−6𝑘 ℓ

= 1

or

Chemistry

5𝑘𝑚=¿¿

smaller unit →bigger number

5𝑘𝑚=5𝑘𝑚×( 105𝑐𝑚1𝑘𝑚 )=5×105𝑐𝑚

= 1

5𝑘𝑚=5𝑘𝑚×( 1𝑚1𝑚 )=5𝑘𝑚×( 102𝑐𝑚

10− 3𝑘𝑚 )=5×105𝑐𝑚or

or

or5𝑘𝑚=5𝑘𝑚×( 103𝑚

1𝑘𝑚 )( 1𝑐𝑚10−2𝑚 )=5×105𝑐𝑚 Chemistry

= 1

= 1

The wavelenagth of green light is 500 nm. How many meters is this?

Practice individually. You have 5 minutes.

larger unit is “m” “1m” in numerator

start: nmend: m

500𝑛𝑚×( 1𝑚109𝑛𝑚 )=500×10− 9𝑚=5×10− 7𝑚

or 1𝑛𝑚=10− 9𝑚500𝑛𝑚=500×10−9𝑚=5×10−7𝑚

I have 906 gigabyte hard drive on my computer. How many bytes of data will it hold?

906𝐺𝑏𝑦𝑡𝑒𝑠=906×109𝑏𝑦𝑡𝑒𝑠=9.06×1011𝑏𝑦𝑡𝑒𝑠

How many liters is 16 ℓ ?

16𝜇 ℓ=1.6×10−5 ℓ4.3 x 104 ns = ? µs

4.3 = 43 µs1

5.2 x 108 ms = ? ks

5.2×108𝑚𝑠=520𝑘𝑠1 ms = 10-6 ks

DID YOU KNOW?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 a red blood cell ≈ 8 μm

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 Earth ≈ 13 Mm

Diameter of sun ≈ 1.4 Gm

Diameter of Milky Way ≈ 9500 Tm

visible universe is thought to be around 1025 mScale of the Universe

http://htwins.net/

Time, length, and weight are all separate dimensions You can only convert between measurements within the same

dimensionFor example: Time can be measured in seconds, minutes, or hours You CAN convert seconds minutes hours You CANNOT convert seconds centimeters

PHYSICAL QUANTITIES:

Anything you measure or calculate in physicsPhysical quantities are expressed in UNITS

What is DIMENSION of a physical quantity?

What is difference between dimension and unit of a physical quantity?

What is physical quantity?

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

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)

SI Units

In short : Nature of the beast (physical quantity) is dimension (quality).To express the quantity of the beast we need units.

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)

BasicPhysical Quantity

BasicSI Unit

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.

BasicDimension

DerivedPhysical Quantityarea L2 m2

volume L3 m3

speed L/T m/sacceleration L/T2 m/s2

forceML/T2 kg.m/s2

newton (N)power M L2/T3 kg.m2/s3

watt (W)mass density

M/ L3 kg/m3

DerivedDimension

Derived SI Unit

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

Which one of the following quantities are dimensionless (and therefore unitless)?

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.

1 kg is basic unit of mass,not, I repeat, not 1g !!!!!!!!!!

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

2. acceleration (velocity/time)

3. density (mass/volume)

4. force (mass × acceleration)

5. charge (current × time)

6. Height

7. pressure (force/area)

8. work (force × distance)

L3, m3

L/T2, m/s2

M/L3, kg/m3

M•L/T2, kg•m/s2

I•T, A•s

L, m

M/(L•T2), kg/(m•s2)

M•L2/T2, kg•m2/s2

DIMENSION ANALISYS: LSequation = RSequation both units and dimensions

Determine if the following equation is dimensionally correct.

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

½ is number, it cannot be measured → no unit

𝐿=𝐿+ 𝐿𝑇 𝑇+𝐿𝑇 2 𝑇

2

Which of the following most accurately describes the velocity of 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

( 𝐿𝑇 2 𝐿  )1 /2

=𝐿𝑇

𝐿𝑇2 𝐿=

𝐿2

𝑇 2

( 𝐿𝑇 2 𝐿  )1 /2

=𝐿𝑇

𝑀 𝐿𝑇 2 𝐿=𝑀 𝐿2

𝑇 2

we don’t know without further informationboth A) and C) are dimensionaly correct

Practice time

1𝑚3=1(102𝑐𝑚)3=106𝑐𝑚3

1𝑚3=1(103𝑚𝑚)3=109𝑚𝑚3

1𝑐𝑚3=1(10− 2𝑚)3=10−6𝑚3

1𝑚𝑚3=1(10− 3𝑚)3=10− 9𝑚3

7.2 m3 → mm3 7.2𝑚3=7.2 (103𝑚𝑚)3 = 7.2  x 109  𝑚𝑚3

75 g/cm2 → kg/m2

100 mm3 → m3 100𝑚𝑚3=100 (10−3𝑚)3=10− 7𝑚3

75

72 km/h → m/s

20 = 20 = 72 km/h20 m/s → km/h

72 = 20 m/s

75

20 =20 = 72 km/h

72 = 20 m/s

7.2 m3 → mm3 7.2𝑚3=7.2 (103𝑚𝑚)3 = 7.2  x 109  𝑚𝑚3

75 g/cm2 → kg/m2

100 mm3 → m3 100𝑚𝑚3=100 (10−3𝑚)3=10− 7𝑚3

75

60 mi/h = ? m/s1 mi = 1609 m

60 = 27 m/s

72 km/h → m/s

20 = 20 = 72 km/h20 m/s → km/h

72 = 20 m/s

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:

No measurement can be "exact". You can never, NEVER get exact value experimentally

Uncertainty and error in measurement

The inevitable uncertainty is inherent in measurements. It is not to be confused with a mistake or blunder

precise, not accurate

accurate, not precise

neither precise, nor accurate

both 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. -

● 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.

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 m

52 m – reliably known0.8 mis uncertain – estimate

• No measurement can be "exact". This would require a measuring instrument with marks infinitely close together – which is clearly impossible.

☞ 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

97.329 - 47.54 = (49.789) = 49.80 (3 dec) - (2 dec) = (2 dec) Answer should be reported with 2 dec only

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.

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

Multiplication, Division, Powers and Roots: