Education is what remains after one has forgotten what one has learned in school.

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1 1 Education is what remains after one has forgotten what one has learned in school. It's not that I'm so smart; it's just that I stay with problems longer. The study of matter, energy, and the interactions between them in other words, everything! 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 = mc 2 ). 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. 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. The model must be expressed in human terms. Our models speak as much about us, our experience and our modes of thought as they do about the external reality being modeled. Point object: We know everything about the motion if we know the position and the velocity of that object at any time. Questions: Do all points on the ball follow the same path at the same time? hammer: Do legs follow the same path as the head? This is the combination of rotation (around its center of mass) and the motion along a line - parabola.

2 Motion of an object can be very complicated and complex. In order to describe the motion of an object in mathematical language we have to introduce the model of the object, simplifying complicated situations. Look at the center of mass of the hammer. The path is very simple: parabola The simplest model: we choose to ignore everything that is not important (color) or too complicated (shape, size, spin, relative motion of the body parts, air resistance). The systems we are going to study will be treated as POINT OBJECTS. 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 as a small circle. Now, our hammer is a point and follows parabola path. 2 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 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: 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 (Theory supported by math) (hypothesis) (Law of Evolution) (Theory of Natural Selection) Scientific Notation Why do we use Scientific Notation? The mass of the Earth is kg. Much better way: X kg Swine flu virus: diameter of 10 to 300 nanometers (nanometer is equal to one billionth of a meter) m becomes 1.0 x m in scientific notation pretty decent We use Scientific Notation or Prefixes when dealing with numbers that are very small or very big. Examples: 1. The best estimate of the age of the universe is years = years = 13.7 billion years scientific notation 2. electron mass = kg = kilograms m = 3.54 x 10-3 m = 3.54 mm prefix Another reason to use Scientific Notation? For showing the precision of a measurement. 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 10 2 lbs, the precision is clear it is between 201 and 199. More on this, later!

3 3 Prefixes & SI UNIT CONVERSIONS Every step is 10 ± 1 power They are grouped into steps 10 ± 3 Unit conversions involving SI unit prefixes smaller unit bigger number larger unit smaller number 5 kkl = kkl 5 kkkk = cckk 5 kkl = 5 kkl 1kkl 10 6 kkl = kkl 5 kkkk = 5kkkk 105 cckk 1kkkk = cckk = 1 = 1 or 1kkkk = 10 5 cccc or 1kkkk = 10 5 cccc 5kkkk = cccc 5kkkk = cccc The wavelength of green light is 500 nm. How many meters is this? 500 nkk 1kk 10 9 nkk = kk = kk or 1 nkk = 10 9 kk 500 nkk = kk = kk start: nm end: m larger unit is m 1m in numerator

4 I have 906 gigabyte hard drive on my computer. How many bytes of data will it hold? Gbytes = bytes = bytes How many liters is 16 μl? 4.3 x 10 4 ns =? µs 5.2 x 10 8 ms =? ks 16 μl = l 1 ns = 10 3 μs 1 ms = 10-6 ks ns = 43 µs kks = 520 kks 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 = 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 What is physical quantity? What is DIMENSION of a physical quantity? What is the difference between dimension and unit of a physical quantity? PHYSICAL QUANTITIES 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 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 L 2 since area can always be calculated as a length times a length.

5 Confusing????? Dimension of physical quantity distance is length. Dimension of speed is length/time 5 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 Derived Physical Quantity Derived Dimension Derived SI Unit Distance, Length (L) meter (m) height,width 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) area L 2 m 2 volume L 3 m 3 speed L/T m/s acceleration L/T 2 m/s 2 force ML/T 2 kg. m/s 2 newton (N) power M L 2 /T 3 kg. m 2 /s 3 watt (W) mass density M/ L 3 kg/m 3 Which one of the following quantities are dimensionless (and therefore unitless)? dimensionless 2. sin 68 dimensionless 3. e dimensionless 4. force not dimensionless 5. 6 dimensionless 6. frequency not dimensionless 7. log dimensionless In the study of mechanics, we shall be concerned with physical quantities (and units) that can be described in terms of three fundamental quantities: length (L), time (T), and mass (M). The corresponding basic SI - units are: meter (m), second (s) and kilogram (kg) 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 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. Time 1 second (1s) is defined as 9,192,631,770 times the period of one oscillation of radiation from the cesium atom.

6 DIMENSION ANALISYS: 6 LS equation = RS equation in numbers, units and dimensions Determine the dimensions and corresponding SI units of the following quantities: 1. volume L 3 m 3 2. acceleration (velocity/time) L/T 2 m/s 2 3. density (mass/volume) M/L 3 kg/m 3 4. force (mass acceleration) M L/T 2 kg m/s 2 5. charge (current time) I T, A s 6. Height L m 7. pressure (force/area) M/(L T 2 ) kg/(m s 2 ) 8. work (force distance) M L 2 /T 2 kg m 2 /s 2 Determine if the following equation is dimensionally correct: x = x 0 + v 0 t + (1/2) a t 2 where x is the displacement at time t, x 0 is the displacement at time t = 0, v 0 is the velocity at time t = 0, a is the constant acceleration L = L + L T T + L T 2 T2 L = L ½ is number, it cannot be measured no unit Practice time Practice 1kk 3 = time 1(10 2 cckk) 3 = 10 6 cckk 3 1kk 3 = 1(10 3 kkkk) 3 = 10 9 kkkk 3 1cckk 3 = 1(10 2 kk) 3 = 10 6 kk 3 1kkkk 3 = 1(10 3 kk) 3 = 10 9 kk 3 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 L 1/2 C) (2gh) 1/2 T 2 L = L L 1/2 T T 2 L = L T L L2 B) 2gh D) mgh T2 L = T 2 M L L2 L = M T2 T m 3 mm mm 3 m 3 75 g/cm 2 kg/m 2 20 m/s km/h 72 km/h m/s 60 mi/h =? m/s 1 mi = 1609 m 7.2 kk 3 = kkkk 3 = 7.2 x 10 9 kkkk kkkk 3 = 100(10 3 kk) 3 = 10 7 kk 3 75 g cm 2 = kg (10 2 m) 2 = 750 kg/m 2 20 m = km = 72 km/h s h 72 km = m = 20 m/s h 3600 s 60 mi h = 96 km h 103 m = 27 m/s 3600 s

7 Uncertainty and error in measurement 7 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: 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. -

8 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. 8 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 (digits) Reading: 52.8 ml are reliably known digits + one uncertain 52 ml reliably known 0.8 mluncertain estimate All digits 1,2,3 9 count as significant digits (6 SF) About Zeros: Zeros between other non zero digits are significant (3 SF ), (5 SF) Zeros in front of non zero digits are NOT significant: 0.67 (2 SF), ( 3 SF), (1 SF). Zeros at the beginning merely locate the decimal point. Zeros to the right of a decimal are significant (4 SF), (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 (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, you know that there are only 2 SF, then the result is: m 3 = 34 x 10 3 m 3 So everyone who reads this knows how to interpret it!! 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 you don t know second decimal in the first measurement and third decimal in the second measurement, so the result can not have reliably known second and third decimal = (49.789) = (3 dec) - (2 dec) = (2 dec) Answer has 2 decimals 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 x 5.35 = ( ) = 649 (5 sf) x (3 sf) = (3SF) 2.2?? 1.25? Answer should be rounded only to 3 SF