Topic 1realm Of Physics

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This topic deals with IB physics unit one.
Students of 4CPP and 5CPP must go through it too.

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Topic 1realm Of Physics

  1. 1. Topic 1 Physics and Physical Measurements Contents: 1.1 The realm of physics 1.2 Measurement and uncertainties 1.3 Mathematical and graphical techniques 1.4 Vectors and scalars
  2. 2. Introduction WHAT IS PHYSICS? <ul><li>• Physics (from a Greek term meaning nature ) is historically the term to designate the study of natural phenomena (also natural philosophy till early in the 19th century) </li></ul><ul><li>• Goal of physics: to understand and predict how nature works </li></ul><ul><li>• Everything in nature obeys the laws of physics </li></ul><ul><li>• Everything we build also obeys the laws of physics </li></ul>
  3. 3. PHYSICS & MATHS <ul><li>The laws of physics can be expressed in terms of mathematical equations </li></ul><ul><li>MOTION WITH CONSTANT VELOCITY </li></ul><ul><li>x = vt </li></ul><ul><li>space velocity time </li></ul><ul><li>Prediction from theory Observation from experiments </li></ul>
  4. 4. MEASUREMENTS <ul><li>allow us to make quantitative comparisons </li></ul><ul><li>between the laws of physics and the natural </li></ul><ul><li>world </li></ul><ul><li>Common measured quantities: length, mass, </li></ul><ul><li>time, temperature … </li></ul><ul><li>A measurement requires a system of units </li></ul><ul><li>Measurement = number x unit </li></ul>
  5. 5. THE INTERNATIONAL SYSTEM OF UNITS (SI)* <ul><li>The 11th Conférence Générale des Poids et Mesures (1960) adopted the name Système International d'Unités (International System of Units, SI), for the recommended practical system of units of measurement. </li></ul><ul><li>The 11th CGPM laid down rules for the base units , the derived units , prefixes and other matters. </li></ul><ul><li>The SI is not static but evolves to match the world's increasingly demanding requirements for measurement </li></ul><ul><li>* Also mks </li></ul>
  6. 6. SI BASE UNITS <ul><li>a choice of seven well-defined units which by convention are regarded as dimensionally independent </li></ul><ul><li>Physical quantity unit symbol </li></ul><ul><li>LENGTH meter m </li></ul><ul><li>MASS kilogram kg </li></ul><ul><li>TIME second s </li></ul><ul><li>ELECTRIC CURRENT ampere A </li></ul><ul><li>THERMODYNAMIC TEMPERATURE kelvin K </li></ul><ul><li>AMOUNT OF SUBSTANCE mole mol </li></ul><ul><li>LUMINOUS INTENSITY candela cd </li></ul>
  7. 7. SI BASE UNIT OF LENGTH <ul><li>Previously: 1 meter (from the Greek metron=measure)= </li></ul><ul><li>one ten-millionth of the distance from the North Pole to </li></ul><ul><li>the equator ; standard meter (platinum-iridium alloy rod </li></ul><ul><li>with two marks one meter apart) produced in 1799 </li></ul><ul><li>The meter is the length of the path traveled by light in </li></ul><ul><li>vacuum during a time interval of 1/299,792,458 of a </li></ul><ul><li>second </li></ul>
  8. 8. TYPICAL DISTANCES <ul><li>Diameter of the Milky Way 2x10 20 m </li></ul><ul><li>• One light year 4x10 16 m </li></ul><ul><li>• Distance from Earth to Sun 1.5x10 11 m </li></ul><ul><li>• Radius of Earth 6.37x10 6 m </li></ul><ul><li>• Length of a football field 10 2 m </li></ul><ul><li>• Height of a person 2x10 0 m </li></ul><ul><li>• Diameter of a CD 1.2x10 -1 m </li></ul><ul><li>• Diameter of the aorta 1.8x10 -2 m </li></ul><ul><li>• Diameter of a red blood cell 8x10 -6 m </li></ul><ul><li>• Diameter of the hydrogen atom 10 -10 m </li></ul><ul><li>• Diameter of the proton 2x10 -15 m </li></ul>
  9. 9. SI BASE UNIT OF MASS <ul><li>The kilogram is equal to the mass of the international prototype of the kilogram. </li></ul>Cylinder of platinum and iridium 0.039 m in height and diameter The mass is not the weight (=measure of the gravitational force)
  10. 10. TYPICAL MASSES <ul><li>• Galaxy (Milky Way) 4x10 41 kg </li></ul><ul><li>• Sun 2x10 30 kg </li></ul><ul><li>• Earth 5.97x10 24 kg </li></ul><ul><li>• Elephant 5400 kg </li></ul><ul><li>• Automobile 1200 kg </li></ul><ul><li>• Human 70 kg </li></ul><ul><li>• Honeybee 1.5x10 -4 kg </li></ul><ul><li>• Red blood cell 10 -13 kg </li></ul><ul><li>• Bacterium 10 -15 kg </li></ul><ul><li>• Hydrogen atom 1.67x10 -27 kg </li></ul><ul><li>• Electron 9.11x10 -31 kg </li></ul>
  11. 11. SI BASE UNIT OF TIME <ul><li>Previously: the revolving Earth was considered a fairly accurate timekeeper. </li></ul><ul><li>Mean solar day = 24 h = 24 x 60 min = 24x60x60 s = 84,400 s </li></ul><ul><li>Today the most accurate timekeeper are atomic clock </li></ul><ul><li>(accuracy 1 second in 300,000 years) </li></ul><ul><li>The second is the duration of 9,192,631,770 periods of </li></ul><ul><li>the radiation corresponding to the transition between </li></ul><ul><li>the two hyperfine levels of the ground state of the </li></ul><ul><li>caesium 133 atom. </li></ul>
  12. 12. TYPICAL TIMES <ul><li>• Age of the universe 5 x 10 17 s </li></ul><ul><li>• Age of the Earth 1.3 x 10 17 s </li></ul><ul><li>• Existence of human species 6 x 10 13 s </li></ul><ul><li>• Human lifetime 2 x 10 9 s </li></ul><ul><li>• One year 3 x 10 7 s </li></ul><ul><li>• One day 8.6 x 10 4 s </li></ul><ul><li>• Time between heartbeat 0.8 s </li></ul><ul><li>• Human reaction time 0.1 s </li></ul><ul><li>• One cycle of a high-pitched sound </li></ul><ul><li>wave 5 x 10 -5 s </li></ul><ul><li>• One cycle of an AM radio wave 10 -6 s </li></ul><ul><li>• One cycle of a visible light wave 2 x 10 -15 s </li></ul>
  13. 13. SI BASE UNIT OF TEMPERATURE <ul><li>The kelvin , unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water . </li></ul><ul><li>The triple point of any substance is that temperature and pressure at which the material can coexist in all three phases (solid, liquid and gas) at equilibrium. </li></ul>
  14. 14. SI DERIVED UNITS <ul><li>formed by combining base units according to the </li></ul><ul><li>Algebraic relations linking the corresponding </li></ul><ul><li>quantities </li></ul><ul><li>Physical quantity unit equivalent </li></ul><ul><li>FREQUENCY Hertz Hz = 1/s=s -1 </li></ul><ul><li>FORCE Newton N = kg.m.s -2 </li></ul><ul><li>PRESSURE Pascal Pa = N.m -2 = kg. m -1 s -2 </li></ul><ul><li>ENERGY, WORK Joule J = N.m = kg.m 2 .s -2 </li></ul><ul><li>POWER Watt W = J.s -1 = kg.m 2 .s -3 </li></ul>
  15. 15. COMMON SI PREFIXES <ul><li>Power Prefix Abbreviation </li></ul><ul><li>10 15 peta P </li></ul><ul><li>10 12 tera T </li></ul><ul><li>10 9 giga G </li></ul><ul><li>10 6 mega M </li></ul><ul><li>10 3 kilo k </li></ul><ul><li>10 2 hecto h </li></ul><ul><li>10 1 deka da </li></ul><ul><li>10 –1 deci d </li></ul><ul><li>10 –2 centi c </li></ul><ul><li>10 –3 milli m </li></ul><ul><li>10 –6 micro μ </li></ul><ul><li>10 –9 nano n </li></ul><ul><li>10 –12 pico p </li></ul><ul><li>10 –15 femto f </li></ul>
  16. 16. CGS SYSTEM <ul><li>• centimeter cm 1 cm= 10 -2 m </li></ul><ul><li>• gram g 1 g = 10 -3 kg </li></ul><ul><li>• second s </li></ul><ul><li>Derived units </li></ul><ul><li>Energy: erg 1 erg = g.cm 2 .s -2 = 10 -3 kg.10 -4 m 2 .s -2 =10 -7 kg.m 2 .s -2 = 10 -7 J </li></ul><ul><li>Force: dyne 1dyn = 1 erg.cm -1 = 10 -7 J/ 10-2 m =10 -5 N </li></ul>
  17. 17. DIMENSIONAL ANALYSIS <ul><li>dimension = type of quantity independent from units </li></ul><ul><li>1 foot≠ 1.1 mile ≠ 5 km ≠ 2.5 m ≠ 1 light-year </li></ul><ul><li>but </li></ul><ul><li>they have all the same dimension = length </li></ul><ul><li>Any valid formula in physics must be </li></ul><ul><li>dimensionally consistent </li></ul>
  18. 18. DIMENSIONAL ANALYSIS Notation: L length; M mass; T time [M][L 2 ] . [T -2 ] Energy [L] . [T -2 ] Acceleration [L] . [T -1 ] Velocity [L 3 ] Volume [L 2 ] Area [L] Distance DIMENSION QUANTITY
  19. 19. DIMENSIONAL ANALYSIS <ul><li>Dimensional consistency </li></ul><ul><li>distance velocity time distance </li></ul><ul><li>x = vt + x 0 </li></ul>
  20. 20. SIGNIFICANT FIGURES <ul><li>The result of a measurement is known only within a certain accuracy </li></ul><ul><li>• Significant figures are the number of digits reliably known (excluding digits that indicate the decimal place) </li></ul><ul><li>• 3.72 and 0.0000372 have both 3 significant figures </li></ul>
  21. 21. SIGNIFICANT FIGURES <ul><li> Scientific notation </li></ul>3.50 x 10 -3 number of order unity power of ten
  22. 22. SIGNIFICANT FIGURES <ul><li>d=21.2 m </li></ul><ul><li>t=8.5 s </li></ul><ul><li>v=? </li></ul><ul><li>v=d/t=2.4941176 m.s -1 ? </li></ul><ul><li>Rule of thumb (multiplication and division): The number of significant figures after multiplication or division is equal to the number of significant figures in the least accurate known quantity </li></ul>v=d/t=2.5 m.s -1
  23. 23. SIGNIFICANT FIGURES <ul><li>t 1 =16.74s </li></ul><ul><li>t 2 =5.1 s </li></ul><ul><li>t 1 +t 2 =? </li></ul><ul><li>t 1 +t 2 =21.84 s? </li></ul><ul><li>Rule of thumb (addition and subtraction): The number of decimal places after addition or subtraction is equal to the smallest number of decimal places ofany of the individual terms. </li></ul><ul><li> t 1 +t 2 =21.8 s </li></ul>
  24. 24. SIGNIFICANT FIGURES <ul><li>How many significant figures are in </li></ul><ul><li>35.00 </li></ul><ul><li>35 </li></ul><ul><li>3.5x10 -2 </li></ul><ul><li>3.50x10 -3 </li></ul><ul><li> ? </li></ul>4 3 2 2
  25. 25. CONVERTING UNITS <ul><li>You will need to be able to convert from one unit to another for the same quantity. </li></ul><ul><li> Example: </li></ul>Convert 72 km.h -1 to m.s -1
  26. 26. Conversions <ul><li>You will need to be able to convert from one unit to another for the same quantity </li></ul><ul><ul><li>J to kWh </li></ul></ul><ul><ul><li>J to eV </li></ul></ul><ul><ul><li>Years to seconds </li></ul></ul><ul><ul><li>And between other systems and SI </li></ul></ul>
  27. 27. KWh to J and J to eV <ul><li>1 kWh = 1kW x 1 h </li></ul><ul><li>= 1000W x 60 x 60 s </li></ul><ul><li>= 1000 Js -1 x 3600 s </li></ul><ul><li>= 3600000 J </li></ul><ul><li>= 3.6 x 10 6 J </li></ul><ul><li>1 eV = 1.6 x 10 -19 J </li></ul>
  28. 28. SI Format <ul><li>The accepted SI format is </li></ul><ul><ul><li>m.s -1 not m/s </li></ul></ul><ul><ul><li>m.s -2 not m/s/s </li></ul></ul><ul><li>i.e. we use the suffix not dashes </li></ul>
  29. 29. ORDER OF MAGNITUDES <ul><li>An order of magnitude calculation is a rough estimate designed to be accurate to within a factor of about 10 </li></ul><ul><li>To get ideas and feeling for what size of numbers are involved in situation where a precise count is not possible or important </li></ul>
  30. 30. ORDER OF MAGNITUDE <ul><li> TYPICAL DISTANCES </li></ul><ul><li>Diameter of the Milky Way 2x 10 20 m </li></ul><ul><li>• One light year 4x 10 16 m </li></ul><ul><li>• Distance from Earth to Sun 1.5x 10 11 m </li></ul><ul><li>• Radius of Earth 6.37x 10 6 m </li></ul><ul><li>• Length of a football field 10 2 m </li></ul><ul><li>• Height of a person 2x 10 0 m </li></ul><ul><li>• Diameter of a CD 1.2x 10 -1 m </li></ul><ul><li>• Diameter of the aorta 1.8x 10 -2 m </li></ul><ul><li>• Diameter of a red blood cell 8x 10 -6 m </li></ul><ul><li>• Diameter of the hydrogen atom 10 -10 m </li></ul><ul><li>• Diameter of the proton 2x 10 -15 m </li></ul>
  31. 31. ORDER OF MAGNITUDE <ul><li>EXAMPLE </li></ul><ul><li>Estimate the number of seconds in a human </li></ul><ul><li>&quot;lifetime.&quot; </li></ul><ul><li>You can choose the definition of &quot;lifetime.&quot; </li></ul><ul><li>Do all reasonable choices of &quot;lifetime&quot; give answers </li></ul><ul><li>that have the same order of magnitude? </li></ul><ul><li>The order of magnitude estimate: 10 9 seconds </li></ul><ul><li>• 70 yr = 2.2 x 10 9 s </li></ul><ul><li>• 100 yr = 3.1 x 10 9 s </li></ul><ul><li>• 50 yr = 1.6 x 10 9 s </li></ul>
  32. 32. Summary for Range of Magnitudes <ul><li>You will need to be able to state (express) quantities to the nearest order of magnitude, that is to say to the nearest 10 x </li></ul><ul><li>Range of magnitudes of quantities in our universe </li></ul><ul><li>Sizes </li></ul><ul><ul><li>From 10 -15 m (subnuclear particles) </li></ul></ul><ul><ul><li>To 10 +25 m (extent of the visible universe) </li></ul></ul><ul><li>masses </li></ul><ul><ul><li>From 10 -30 kg (electron mass) </li></ul></ul><ul><ul><li>To 10 +50 kg (mass of the universe) </li></ul></ul><ul><li>Times </li></ul><ul><ul><li>From 10 -23 s (passage of light across a nucleus) </li></ul></ul><ul><ul><li>To 10 +18 s (age of the universe) </li></ul></ul><ul><li>You will also be required to state (express) ratios of quantities as differences of order of magnitude. </li></ul><ul><ul><li>Example: </li></ul></ul><ul><ul><li>the hydrogen atom has a diameter of 10 -10 m </li></ul></ul><ul><ul><li>whereas the nucleus is 10 -15 m </li></ul></ul><ul><ul><li>The difference is 10 5 </li></ul></ul><ul><ul><li>A difference of 5 orders of magnitude </li></ul></ul>
  33. 33. Errors and Uncertainties <ul><li>Errors </li></ul><ul><li>Errors can be divided into 2 main classes </li></ul><ul><li>Random errors </li></ul><ul><li>Systematic errors </li></ul>
  34. 34. Mistakes <ul><li>Mistakes on the part of an individual such as </li></ul><ul><ul><li>misreading scales </li></ul></ul><ul><ul><li>poor arithmetic and computational skills </li></ul></ul><ul><ul><li>wrongly transferring raw data to the final report </li></ul></ul><ul><ul><li>using the wrong theory and equations </li></ul></ul><ul><li>These are a source of error but are not considered as an experimental error </li></ul>
  35. 35. Systematic Errors <ul><li>Cause a random set of measurements to be spread about a value rather than being spread about the accepted value </li></ul><ul><li>It is a system or instrument value </li></ul>
  36. 36. Systematic Errors result from <ul><li>Badly made instruments </li></ul><ul><li>Poorly calibrated instruments </li></ul><ul><li>An instrument having a zero error (off-set error), a form of calibration </li></ul><ul><li>Poorly timed actions </li></ul><ul><li>Instrument parallax error </li></ul><ul><li>Note that systematic errors are not reduced by multiple readings </li></ul>
  37. 37. Random Errors <ul><li>Are due to variations in performance of the instrument and the operator . </li></ul><ul><li>Even when systematic errors have been allowed for, there exists error. </li></ul>
  38. 38. Random Errors result from <ul><li>Vibrations and air convection </li></ul><ul><li>Misreading </li></ul><ul><li>Variation in thickness of surface being measured </li></ul><ul><li>Using less sensitive instrument when a more sensitive instrument is available </li></ul><ul><li>Human parallax error </li></ul>
  39. 39. Reducing Random Errors <ul><li>Random errors can be reduced by </li></ul><ul><li>taking multiple readings, and eliminating obviously erroneous result </li></ul><ul><li>or by averaging the range of results. </li></ul>
  40. 40. Accuracy <ul><li>Accuracy is an indication of how close a measurement is to the accepted value indicated by the relative or percentage error in the measurement </li></ul><ul><li>An accurate experiment has a low systematic error </li></ul>
  41. 41. Precision <ul><li>Precision is an indication of the agreement among a number of measurements made in the same way indicated by the absolute error </li></ul><ul><li>A precise experiment has a low random error </li></ul>
  42. 42. uncertainties <ul><li>In any experimental measurement there is always an estimated last digit for the measured quantity. </li></ul><ul><li>You are not certain about the last digit. </li></ul><ul><li>The last digit varies between two extremes expressed as </li></ul><ul><li>Example: a length on a 20cm ruler is expressed as </li></ul>
  43. 43. Expression of physical measurements and uncertainties <ul><li>Any experimental measure is expressed in the form </li></ul>Real value or final value Approximate value or measured value Uncertainty
  44. 44. Types of uncertainties. <ul><li>Absolute uncertainty written as </li></ul><ul><li>Relative uncertainty </li></ul><ul><li>:Percentage uncertainty </li></ul><ul><li>Remark: the absolute uncertainty is always positive </li></ul>
  45. 45. Working with uncertainties. <ul><li>Uncertainty on a sum or difference. </li></ul><ul><li>Rule: in addition or subtraction uncertainties just add </li></ul><ul><li>Uncertainty on a product or a quotient. </li></ul><ul><li>Rule: in a product or a quotient relative or percentage uncertainties add . </li></ul>
  46. 46. Working with uncertainties cont. Or Also for
  47. 47. Limit of Reading and Uncertainty <ul><li>The Limit of Reading of a measurement is equal to the smallest graduation of the scale of an instrument </li></ul><ul><li>The Degree of Uncertainty of a measurement is equal to half the limit of reading </li></ul><ul><li>e.g. If the limit of reading is 0.1cm then the absolute uncertainty range is  0.05cm </li></ul>
  48. 48. Reducing the Effects of Random Uncertainties <ul><li>Take multiple readings </li></ul><ul><li>When a series of readings are taken for a measurement, then the arithmetic mean of the reading is taken as the most probable answer </li></ul><ul><li>The greatest deviation or residual from the mean is taken as the absolute error </li></ul>
  49. 49. Diagramming Accuracy and Precision precise <ul><li>Accurate and precise </li></ul>Accurate
  50. 50. Diagramming Accuracy and Precision in relation to error and uncertainty figure 1
  51. 51. Figure 2
  52. 52. Figure 3
  53. 53. Plotting Uncertainties on Graphs <ul><li>Points are plotted with a fine pencil cross </li></ul><ul><li>Uncertainty or error bars are required </li></ul><ul><li>These are short lines drawn from the plotted points parallel to the axes indicating the absolute error of measurement </li></ul>
  54. 54. Uncertainties on a Graph

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