Unit 0 - The Scientific Method, Quantities and Units PDF

Unit 0 THE SCIENTIFIC METHOD, QUANTITIES AND UNITS. CONTENTS THE SCIENTIFIC METHOD PHYSICAL QUANTITIES AND MEASUREMENT UNITS KINEMATICS: MOVEMENT IN ONE DIMENSION DYNAMICS OF THE MATERIAL POINT WORK AND ENERGY THE SCIENTIFIC METHOD So the experiment is reproductl 1. OBSERVATION: Natural phenome...

Unit 0 THE SCIENTIFIC METHOD, QUANTITIES AND UNITS. CONTENTS THE SCIENTIFIC METHOD PHYSICAL QUANTITIES AND MEASUREMENT UNITS KINEMATICS: MOVEMENT IN ONE DIMENSION DYNAMICS OF THE MATERIAL POINT WORK AND ENERGY THE SCIENTIFIC METHOD So the experiment is reproductl 1. OBSERVATION: Natural phenomena. 2. HYPOTHESIS FORMULATION: Elaboration of an explanation that justifies the studied phenomenon. 3. EXPERIMENTATION: Practical and controlled essays that are systematically repeated. 4. ORGANIZATION OF EXPERIMENTAL DATA: ordering of the experimental data by means of tables, graphs... 5. DRAWING CONCLUSIONS: Comparison and analysis of experimental data to verify the existence of regularities. Scientific laws that are usually expressed mathematically. 6. DEVELOPMENT OF A THEORY: Explanation of a series of observations using laws that offer an interpretation of all of them. Clean correlation but not clear equation : cualitative relation PROBLEM SET 0. INTRODUCTION 1. A researcher is studying the relation between two magnitudes, A and B. The following results are obtained: A 2.00 3.50 5.00 6.50 8.00 B 37.50 21.43 15.00 11.54 9.38 a) With these results, the researcher asserts that A and B are inversely proportional magnitudes. Is this Definition: 1/x statement correct? b) Plot a graph with the values of A as a function of B. What shape has the graph? PROBLEM SET 0. INTRODUCTION 1. A researcher is studying the relation between two magnitudes, A and B. The following results are obtained: A 2.00 3.50 5.00 6.50 8.00 B 37.50 21.43 15.00 11.54 9.38 2.0 40 1/x Data 35 -x e -ax+b 1.5 30 Y B 25 1.0 20 15 0.5 10 5 1 2 3 4 5 A 6 7 8 9 0.0 0 1 2 3 4 5 X 6 7 8 9 PROBLEM SET 0. INTRODUCTION 1. A researcher is studying the relation between two magnitudes, A and B. The following results are obtained: A 2.00 3.50 5.00 6.50 8.00 B 37.50 21.43 15.00 11.54 9.38 1/B 0.0267 0.0467 0.0667 0.0866 0.1066 0.15 Data inverted 1/B 0.10 0.05 0.00 1 2 3 4 5 A 6 7 8 9 PHYSICAL QUANTITIES AND UNITS PHYSICAL QUANTITY Property of which a body possesses a certain amount Can be classified as… EXTENSIVE: value proportional to the amount of matter in the considered body. Volume, kinetic and potential energy, force... INTENSIVE: value independent of the amount of matter in the considered body. Temperature, density, acceleration… ESCALAR: determined by a numerical value and the unit of measure. Mass, temperature, energy… VECTOR: they require modulus, direction and sense to be sufficiently determined together with their respective unit of measure. They are represented by vectors. Speed, acceleration, force... Can be measured by… Comparing its value with another measure of the same quantity previously adopted as a unit of measure PROBLEM SET 0. INTRODUCTION 7. There are two balls which diameters are 20 cm and 1.3·10-4 km. Which of them will have more volume? If the mass of the ball with 20 cm of radius is 500 g and the mass of the other is 10 times less, which ball will have more density? PHYSICAL QUANTITIES AND UNITS UNITS SYSTEM Ordered set of units of measure that have definite and simple relationships with each other. Characteristics…  Reduced number of base quantities. These are self-defining and independent of the others. The base units are the measure of each base quantity.  The derived quantities are obtained by means of mathematical expressions from the basic quantities. In the same way, the derived units are obtained from the base units. International System (SI) Quantities and Base Units of the SI Quantity Unit Symbol Length metre m Mass Kilogram kg Time Second s Electric current intensity Amper A Thermodynamic temperatura Kelvin K Amount of substance Mole mol Luminous intensity Candela cd PHYSICAL QUANTITIES AND UNITS UNITS SYSTEM Ordered set of units of measure that have definite and simple relationships with each other International System (SI)  Use of multiples and submultiples of the system standard unit Multiple Prefix Abbreviation Multiple Prefix Abbreviation 1018 exa E 10-18 atto a 1015 peta P 10-15 femto f 1012 tera T 10-12 pico p 109 giga G 10-9 nano n 106 mega M 10-6 micro µ 103 kilo k 10-3 mili m 102 hecto h 10-2 centi c 101 deca da 10-1 deci d PROBLEM SET 0. INTRODUCTION 7. There are two balls which diameters are 20 cm and 1.3·10-4 km. Which of them will have more volume? If the mass of the ball with 20 cm of radius is 500 g and the mass of the other is 10 times less, which ball will have more density? PHYSICAL QUANTITIES AND UNITS UNITS SYSTEM Ordered set of units of measure that have definite and simple relationships with each other International System (SI)  Simple arithmetic operations are used to define derived quantities and units. Find the dimension of the force magnitude and its unit, the Newton (𝐍), based on the SI base units Newton’s Second Law: 𝐹⃗ = 𝑚 · 𝑎, ⃗ working with quantities 𝐹 = 𝑚 · 𝑎 Let us denote the base quantities mass, length, and time by the symbols M, L, and T, respectively. 𝐹 = M · L · T : dimensions of a derived quantity 𝑁 = kg · m · s Find the dimension of mechanical power and its unit, the watt (𝐖), in terms of SI base units PROBLEM SET 0. INTRODUCTION 2. Find the dimensions of pressure and its units as a function of the base units of the SI. PROBLEM SET 0. INTRODUCTION 10. Prove that the product of mass, acceleration and velocity has dimensions of power. P m a o = . . P ( = L 27 m - = . ↑ (E) (F -x) ( (2) (m a] (2) (m)(= )(2) = = . = · · (F L) . (m · a . o) [m][=][=) = = mate ate = mi = = PHYSICAL QUANTITIES AND UNITS UNITS SYSTEM Ordered set of units of measure that have definite and simple relationships with each other Based on centimeter, gram and second. The unit of force is the dyne and the unit of energy is the erg. Unit of length, the foot; unit of force, the pound. CGS System "Hercio English System CNMGE CHANGING UNITS  Determine equivalencies.  Convert units into others using conversion factors. 𝒄𝒂𝒍 𝑱 𝒂𝒕𝒎·𝑳 Find the value of the ideal gas constant in 𝒎𝒐𝒍·𝑲 and 𝒎𝒐𝒍·𝑲 , knowing that 𝑹 = 𝟎. 𝟎𝟖𝟐 𝒎𝒐𝒍·𝑲 - equivalencies: 1 𝐽 = 0.00987 atm · L and 1 cal = 4.187 J · - Solution: 𝑅 = 0.082 · = 1.987207 · = 8.314472 · Express the energy unit 𝐉 and 𝐜𝐚𝐥 based on the base units of the SI () (f (] (m () = . = . a . = (m) (=]() = me = 15 = Tery kym gm = PROBLEM SET 0. INTRODUCTION 6. Make the following change of units: a) 850mm to m c) 150 cm3 to m3 b) 1997 weeks to seconds d) 760 kg/m3 to g/cm3 PHYSICAL QUANTITIES AND UNITS SCIENTIFIC NOTATION 0.000002 kg = 2 · 10 MAGNITUDE ORDER Height of an ant: 8 · 10 SIGNIFICANT FIGURES • • • • • Express each number by means of an integer part of a non-zero figure, a decimal part and a power of 10 of integer exponent. kg; 45200000 m = 4.52 · 10 m Number rounded to the nearest power of 10. m; magnitude order: 10 m All those numbers known with certainty of a certain value plus the first one that is considered doubtful It is different from zero: 𝟖𝟕𝟐𝟑 → 4 SF Zeros between SF are also SF: 𝟏𝟎𝟓 → 3 SF Zeros to the left of the first SF are not SF: 𝟎. 𝟎𝟎𝟐 → 1 SF For numbers greater than 1, the zeros to the right of the decimal separator are SF: 𝟔. 𝟎𝟎 → 3 SF. For numbers without a decimal separator, zeros after the last nonzero digit may or may not be considered significant. This ambiguity is avoided by using scientific notation 𝟕 · 𝟏𝟎 𝟐 → 1 SF 𝟕. 𝟎 · 𝟏𝟎 𝟐 → 2 SF PROBLEM SET 0. INTRODUCTION 5. Express the following numbers in scientific notation: a) 5720 ~ 5 72 . . 103 c) 53000000000 ~ - - . 3 1010 5 . b) 0.0027 ~ 27 . 183 ~d) 0.0000741 7 41 . . 10-5 e) 527380000000 v - 5 2738 . - . 101 f) 0.00000000096 - - - 9 . 6 18 .