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# 3 e physcial quantities and units_pure_upload

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### 3 e physcial quantities and units_pure_upload

1. 1. Specific InstructionalObjectivesAt the end of the lesson, you should be able to: show understanding that all physical quantities consists of a numerical magnitude and a unit. Recall the following base quantities and their units mass (kg), length (m), time (s), current (A), temperature (K) amount of substance (mol) use the following prefixes and their symbols to indicate decimal sub-multiples and multiples of the SI units: nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M) show an understanding of the orders of magnitude of the sizes of common objects ranging from a typical atom to the Earth state what is meant by scalar and vector quantities and give common examples of each add two vectors to determine a resultant by a graphical method describe how to measure a variety of lengths with appropriate accuracy by means of tapes, rules, micrometers and calipers, using a vernier scale as necessary describe how to measure a short interval of time including the period of a simple pendulum with appropriate accuracy using stopwatches or appropriate instruments
2. 2. Unit 1: PhysicalQuantities and Units
3. 3. Specific InstructionalObjectivesAt the end of the lesson, you should be able to:1. show understanding that all physical quantities consists of a numerical magnitude and a unit.2. Recall the following base quantities and their units mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)
4. 4. 1.1 Physical Quantities Quantitative vs Qualitative (Measurements vs Descriptions)•Scientists do not use descriptions to make observations as these would most likely cause disagreements.•“How large is large?” or “How small is small?”•Instead, sizes are specified using a number and a standard unit such as the metre.
5. 5. What is a Physical Quantity???Definition: A physical quantity is one that can be measured and that consist of a numerical magnitude and a unit. Examples include length, volume, time and temperature. What other physical quantities can you think of?
6. 6. Magnitude and Unit All physical quantities consists of a numerical magnitude (size) and a unit. E.g. My height = 1.76 m E.g. The temperature today is 29 oC
7. 7. Base Quantity There are 7 base quantities. All the other quantities (derived quantities) can be worked out from the 7 base quantities. Base Quantities Why are these 1. Length quantities called 2. Mass base quantities? 3. Time 4. Temperature 5. Electric current 6. Luminous intensity 7. Amount of substance
8. 8. SI units French ‘Le Systeme International d’ Unites’ English translation: ‘International System of units’ This set of units is internationally accepted/agreed by scientist Imperial Units versus Metric Units
9. 9. 7 Base Quantities and their SI UnitsBase Quantities SI units1. Length (l) metre (m)2. Mass (m) kilogram (kg)3. Time (t) second (s)4. Temperature (T) kelvin (K)5. Electric current (I) ampere (A)6. Luminous intensity (Iv) candela (cd)7. Amount of substance mole (mol)(n) http://physics.nist.gov/cuu/Units/index.html
10. 10. SI Units of derived quantitiesExample(a) Area = length × breadth m m ∴SI unit of area = m × m = m 2 mass kg(b) density = volume m3 ∴SI unit of density = kg/m 3 (or kgm -3 )
11. 11. 1.2 SI Units Derived QuantitiesDerived quantities Symbol for unit Special namearea m2volume m3density kg m−3speed m s—1acceleration m s—2force kg m s—2 (N) newton (N)pressure kg m−1 s−2(N m−2) pascal (Pa)work kg m2 s−2 (N m) joule (J)power Kg m2 s−3 (J s−1) watt (W)
12. 12. Quick Check1. Name the base quantities and identify their SI units.
13. 13. Theory WorkbookExercise 1.1 (page 1)Q1 and Q2
14. 14. Specific InstructionalObjectivesAt the end of the lesson, you should be able to:1. use the following prefixes and their symbols to indicate decimal sub-multiples and multiples of the SI units: nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M)2. show an understanding of the orders of magnitude of the sizes of common objects ranging from a typical atom to the Earth
15. 15. Understanding prefixes kilogram prefix kilo = 103 = 1000 Therefore 1 kilogram = 1000 gram1 km = ________m 1 kJ = ________J
16. 16. Understanding prefixes centimetre prefix centi = 10-2 = 0.01 Therefore 1 centimetre = 0.01 metre
17. 17. Common Prefixes Factor Name 109 Giga (G) 106 mega (M) 103 kilo (k) 10-1 deci (d) 10-2 centi (c) 10-3 milli (m) 10-6 micro (µ) 10-9 nano (n)
18. 18. Why do we needExample prefixes?Write(a) 50 megawatts (MW) in watts (W)(b) 250 nanoseconds (ns) in seconds (s) (a ) 50 MW = 50 × 10 6 W = 50000000 W −9 (b) 250ns = 250 × 10 s = 0.00000025 s
19. 19. Approximate length of some objectsDistance from Earth to Sun 1.5 x 1011 mRadius of the Earth 6 x 106 mHeight of Mount Everest 1 x 104 mLength of a football field 1 x 102 mheight of a 4 year-old child 1mlength of a bee 6 x 10-3 mdiameter of a strand of hair 1 x 10-4 mdiameter of a hydrogen 6 x 10-10 matom
20. 20. Quick Check1. Rewrite the following quantities using suitable prefixes. (a) 5 000 000 J 5 MJ (b) 48 000 g 48 kg (c) 0.0009 s 900 µs or 0.9 ms
21. 21. Theory WorkbookExercise 1.1 (page 1)Q3
22. 22. The Standard FormMany measurements in modern scientificfields involve very large and very smallnumbers.E.g.Speed of light = 300 000 000 m/swavelength of violet light = 0.00000038 mIt is troublesome to write many zeroes forvery large and very small numbers.
23. 23. The Standard FormHence mathematicians/scientists decided to use amore convenient known as the standard form: E.g 3 00 000 000 can be written as 3.0 × 100 000 000 = 3.0 × 108 m/s (standard form) The standard form is always written as A × 10n, Where 1 < A < 10 and n is an integer
24. 24. Which of these figures in standard form? 0.5 × 106 1.002 × 105 2.6 × 103 105 × 108 9.9 × 10-8
25. 25. The Standard FormExample: Express the following as standardform:(i) 4.0 0 0 0 0 = 4.0 × 105(ii) 3 .4 5 0 0 0 0 = 3.45 × 106
26. 26. The Standard FormExample: Express the following as standardform:(i) 2.2 2 0 = 2.22 × 103(ii) 1 .0 1 = 1.01 × 102
27. 27. The Standard FormVery small numbers can also be written asstandard form: For example 0.038 can be written as 3.8 × 10-2 A × 10n
28. 28. The Standard FormExample: Express the following as standardform:(i) 0. 0 0 0 0 1. 2 5 = 1.25 × 10-5(ii) 0. 0 0 0 3 . 4 = 3.4 × 10-4
29. 29. The Standard FormExample: Express the following as standardform:(i) 0. 0 0 0 0 0 2. 2 3 = 2.23 × 10-6(ii) 0. 0 1. = 1.0 × 10-2
30. 30. The Standard FormExample: Express the following in ordinarynotation:(a) 1.25 × 103(b) 4.3 × 106(c) 2.6 × 10-3(d) 8.7 × 10-5
31. 31. Theory WorkbookExercise 1.1 (page 1)Q4
32. 32. Prefix and standard form50,000,000 W= 50MW (prefix)= 5 x 107 W (standard form) Both prefixes and use of standard form reduces the need to write many zeros. Which is better?
33. 33. Specific InstructionalObjectivesAt the end of the lesson, you should be able to:1. describe how to measure a variety of lengths with appropriate accuracy by means of tapes, rules, micrometers and calipers, using a vernier scale as necessary.
34. 34. Measurement of lengthsWhich instrument would you use to measurethe length of a pencil? A 15-cm or 30-cm rule
35. 35. Measurement of lengthsWhich instrument would you use to measurethe length of your desk? A metre rule
36. 36. Measurement of lengthsWhich instrument would you use to measurethe length of a room? A measuring tape
37. 37. Measurement of lengthsWhich instrument would you use to measurethe length of a school field?
38. 38. Measurement of lengthsWhich instrument(s) would you use to measurethe thickness of a pencil? 0.922 cm 0.9 cm 0.92 cm Micrometer ruler Vernier calipers screw gauge
39. 39. Measurement of LengthMeasuring Instrument Range PrecisionMeasuring tape 0–5m 0.1 cmMetre rule 0–1m 0.1 cmVernier calipers 0 – 15 cm 0.01 cmMicrometer 0 – 2.5 cm 0.001 cmscrew gauge
40. 40. Quick CheckWhich instruments would you use to measure the lengthsof the following? Diameter of a Internal diameter Length of your strand of hair of a mug textbook
41. 41. Vernier Calipers
42. 42. Vernier Calipers mm 23 6 Measured value is between 23 and 24 mm 6 = 23. __ mm
43. 43. Vernier Calipers 2.9_ cm 4 Vernier scale 0 5 100 cm 3 cm 4 cm Main scale
44. 44. Theory WorkbookExercise 1.3 (page 3)Q4(a) 3.43 cm(b) 1.39 cm
45. 45. Parts of a vernier calipers inner jaws Depth bar Outer jaws
46. 46. 1.5 Measurement of Length and TimeAccurate Measurement • Two main types of errors Random errors Systematic errors Random errors because they Not random but constant are unpredictable They arise when observers Due to the equipment being estimate the last figure of a used – e.g. a ruler with zero reading on an instrument. error Minimized by averaging a Cannot be reduced by large number of readings averaging, but they can be eliminated if the sources of the errors are known
47. 47. Zero Error on a Vernier Scale What is Zero Error???Definition:If the zero marks on the main scale and vernier scaledo not coincide when the jaws are closed, there is azero error.
48. 48. Zero Error Subtracted from Reading 4th line after zero on vernier scale coincides with line on main scale: zero error = 0.04 cm Zero error is subtracted from the reading
49. 49. Zero Error Added to Reading7th line after zero on vernier scalecoincides with line on main scale:Zero error = 0.1 – 0.07 = 0.03 cm
51. 51. Zero Error Added to Reading7th line after zero on vernier scalecoincides with line on main scale:Zero error = 0.1 – 0.07 = 0.03 cm Zero error is ‘added’ to the reading Note: By convention, ‘under-read’ zero error is negative, i.e. the zero error in this case is – 0.03 cm.
52. 52. Textbook Read TB pg 13
53. 53. Example Zero errorReading = +0.08 cmwhen jawsare closed Reading on scale = 0.64 cmReading when jaws Thickness of coinare used to measure = 0.64 – 0.08the thickness of acoin = 0.56 cm
54. 54. Example 0 5 10 Zero error 0 1 cm = - 0.02 cm Reading when jaws are closed 0 5 10 Reading on scale = 0.84 cm 1 cm 2 cm Thickness of coin = 0.84 – (- 0.02) Reading when jaws are used to measure the thickness of a coin = 0.86 cm
55. 55. The micrometer screw gaugehttp://members.shaw.ca/ron.blond/Micrometer.APPLET/
56. 56. The micrometer screw gauge 0.14 mm mm 5.5 mm Reading = main scale R + thimble scale R = 5.5 + 0.14 = 5.64 mm
57. 57. The micrometer screw gauge mm 5.14 mm
58. 58. The micrometer screw gauge 35 30 mm 25 7.29 mm
59. 59. The micrometer screw gauge 35 30 25 3.79 mm
60. 60. The micrometer screw gauge 45 40 35 4.39 mm
61. 61. The micrometer screw gauge 45 40 35 6.89 mm
62. 62. Theory WorkbookExercise 1.3 (page 3)Q5(a) 4.13 mm(b) 2.79 mm
63. 63. Precautions when using amicrometer Avoid over-tightening  use the ratchet for fine adjustment Clean the ends of anvil and spindle before measuring. Check for zero-error (read TB page 14)
64. 64. Zero-error
65. 65. Theory WorkbookExercise 1.3 (page 3)Q6Zero error = -0.02 mmReading on scale = 1.19 mmThickness of the coin = 1.19 – (-0.02)= 1.21 mm
66. 66. Specific InstructionalObjectivesAt the end of the lesson, you should be able to:1. describe how to measure a short interval of time including the period of a simple pendulum with appropriate accuracy using stopwatches or appropriate instruments
67. 67. How to measure time?
68. 68. http://www.phy.ntnu.edu.tw/oldjava/pendulum30/pendulum.htmlA simple pendulum Pendulum.mht http://www.fearofphysics.com/Pendulums/pendhl.html 1 oscillation =A–O–B–O–A Or: 1 oscillation =O–B–O–A-OThe Period (T) of apendulum is thetime taken for 1completeoscillation. A B O
69. 69. Pendulum Lab
70. 70. Stop Watches Human Reaction Time: 0.3 s
71. 71. Theory WorkbookExercise 1.3 (page 3-4)Q1Q9Q10Q111 (a) Metre rule; (b) vernier calipers; (c) micrometer screw gauge; (d) zero error; (e) period9 28.4 s; 2 min 25.6 s; 2 min 55.6 s10 34.26 s; 1 min 23.48 s11 (a) 0.64 s; (b) 0.16 s; (c) The period of oscillatoin increases
72. 72. Ticker-Tape Timer Frequency: 50 dots per second 1 S 50
73. 73. Class Practice/ HomeworkSelf-Management (TB page 23)Misconception Analysis  Q1 – 10Practice (TB page 23 – 25)Q3 and 4Q1 on unit conversion is a bit challenging(optional)