1. 1 Honors Physics A Physics Toolkit

2. 2 Honors Physics Chapter 1 Turn in Contract/Signature Lecture: A Physics Toolkit Q&A Website: http://www.mrlee.altervista.org

3. 3 The Metric System Physics is based on measurement. International System of Units (SI unit) – Fundamental (base)quantities: more intuitive – Derived quantities: can be described using fundamental quantities.  length, time, mass …  Speed = length / time  Volume = length 3  Density = mass / volume = mass / length 3 Two kinds of quantities: – Created by French scientists in 1795.

4. 4 Units Unit: a measure of the quantity that is defined to be exactly 1.0. Fundamental (base) Unit: unit associated with a fundamental quantity Derived Unit: unit associated with a derived quantity – Combination of fundamental units

5. 5 Units Standard Unit: a unit recognized and accepted by all. QuantityUnit NameUnit Symbol LengthMeterm TimeSeconds Masskilogramkg Some SI standard base units – Standard and non-standard are separate from fundamental and derived.

6. 6 Prefixes Used With SI Units PrefixSymbolFractions nanon  10 -9 micro  10 -6 millim  10 -3 centic  10 -2 kilok  10 3 megaM  10 6 gigaG  10 9

7. 7 Conversion Factors 1 m = 100 cm so and Conversion factor: or Which conversion factor to use?  Depends on what we want to cancel.

8. 8 Example 2.1 km = ____ m Not good, cannot cancel Given: 1 km = 1000 m

9. 9 Practice 12 cm = ____ m

10. 10 Chain Conversion 1.1 cm = ___ km

11. 11 Practice 7.1 km = ____ cm

12. 12 Still simple? How about… 2 mile/hr = __ m/s Chain Conversion

13. 13 When reading the scale, Estimate to 1/10 th of the smallest division 11 cm.5 1.3 cm – Draw mental 1/10 divisions – However, if smallest division is already too small, just estimate to closest smallest division. but not 1.33 cm, why?

14. 14 Uncertainty of Measurement All measurements are subject to uncertainties.  External influences: temperature, magnetic field  Parallax: the apparent shift in the position of an object when viewed from different angles. Uncertainties in measurement cannot be avoided, although we can make it very small by using good experimental skills and apparatus. Uncertainties are not mistakes; mistakes can be avoided. Uncertainty = experimental error

15. 15 Precision Precision: the degree of exactness to which a measurement can be reproduced. The precision of an instrument is limited by the smallest division on the measurement scale. Smaller uncertainty = more precise Larger Uncertainty = less precise – Uncertainty is one-tenth of the smallest division.  Typical meter stick: Smallest division is 1 mm = 0.001 m, uncertainty is 0.1 mm = 0.0001m. – A typical meterstick can give a measurement of 0.2345 m, with an uncertainty of 0.0001 m.

16. 16 Accuracy Accuracy: how close the measurement is to the accepted or true value Accuracy  Precision Accepted (true) value is 1.00 m. Measurement #1 is 0.99 m, and Measurement #2 is 1.123 m. – ____ is more accurate: #1 #2 closer to true value – ____ is more precise:uncertainty of 0.001 m (compared to 0.01 m) more precise more accurate

17. 17 Significant Figures (Digits) 1. Nonzero digits are always significant. 2. The final zero is significant when there is a decimal point. 3. Zeros between two other significant digits are always significant. 4. Zeros used solely for spacing the decimal point are not significant. Example:  1.002300  0.004005600  7 sig. fig’s  12300  3 sig. fig’s  12300.  5 sig. fig’s

18. 18 Practice: How many significant figures are there in a) 123000 b) 1.23000 c) 0.001230 d) 0.0120020 e) 1.0 f) 0.10

19. 19 Operation with measurements In general, no final result should be “more precise” than the original data from which it was derived.

20. 20 Addition and subtraction with measurements The sum or difference of two measurements is precise to the same number of digits after the decimal point as the one with the least number of digits after the decimal point. Example: 16.26 + 4.2 = 20.46  Which number has the least digits after the DP?  4.2  Precise to how many digits after the DP?  1 1  So the final answer should be rounded-off (up or down) to how many digits after the DP?  1 1 =20.5

21. 21 Practice: 1) 23.109 + 2.13 = ____ 2) 12.7 + 3.31 = ____ 3) 12.7 + 3.35 = ____ 4) 12. + 3.3= ____ 1) 23.109 + 2.13 = 25.239 = 25.24 2) 12.7+3.31 = 16.01 = 16.0 Must keep this 0. 3) 12.7+3.35 = 16.05 = 16.1 4) 12. + 3.3 = 15.3 = 15. Keep the decimal pt.

22. 22 Multiplication and Division with measurements The product or quotient has the same number of significant digits as the measurement with the least number of significant digits. Example: 2.33  4.5 = 10.485  Which number has the least number of sig. figs?  4.5  How many sig figs does it have?  2 2  So the final answer should be rounded-off (up or down) to how many sig figs?  2 2 =10.

23. 23 Practice: 2.33/3.0 = ___ 2.33 / 3.0 = 0.7766667 = 0.78 2 sig figs

24. 24 What about exact numbers? Exact numbers have infinite number of sig. figs. If 2 is an exact number, then 2.33 / 2 = __ 2.33 / 2 = 1.165 = 1.17 Note: 2.33 has the least number of sig. figs: 3

25. 25 Scientific Notation Whenever it becomes awkward to say a number, use scientific notation. 4 times to the left 4 times to the right M  10 n Example:  1 <= |M| < 10  n: exponent (positive, zero, or negative integer) 23000 = 2.3  10 4 0.00032 = 3.2  10 -4

26. 26 Practice 860000 = _________ 0.0000102 = ________ 30000000 = ________ 0.0000003 = ________ 8.6 × 10 5 1.02 × 10 -5 3 × 10 7 3 × 10 -7

27. 27 Arithmetic Operations in Scientific Notation Adding and subtracting with like exponents Adding and subtracting with unlike exponents Adding and subtracting with unlike units Multiplication using scientific notation Division using scientific notation Use calculator. Skip to Slide 36

28. 28 Adding and subtracting with like exponents Add or subtract the values of M and keep the same n. Example: 2  10 5 m + 3  10 5 m = (2 + 3)  10 5 m = 5  10 5 m 5.3  10 4 m – 2.1  10 4 m = (5.3 – 2.1)  10 4 m = 3.2  10 4 m

29. 29 Practice:

30. 30 Adding and subtracting with unlike exponents 1. First make the exponents the same. 2. Then add or subtract. 2.0  10 3 m + 5  10 2 m = 2.0  10 3 m + 0.5  10 3 m = (2.0 + 0.5)  10 3 m = 2.5  10 3 m

31. 31 Practice:

32. 32 Adding and subtracting with unlike units 1. Convert to common unit 2. Make the components the same 3. Add or subtract Example: 2.10 m + 3 cm = 2.10 m + 0.03 m = 2.13 m

33. 33 Multiplication using scientific notation 1. Multiply the values of M 2. Add the exponents 3. Units are multiplied (3  10 4 kg)  (2  10 5 m) = (3  2)  10 4+5 (kg  m) = 6  10 9 kg × m

34. 34 Practice:

35. 35 Division using scientific notation 1. Divide the values of M. 2. Subtract the exponent of the divisor from the exponent of the dividend. 3. Divide the unit of the divisor from the unit of the dividend.

36. 36 Displaying Data Table Graph  Independent variable: manipulated  Dependent variable: responding

37. 37 Table Title or description Variables (quantities) Unit (either after variables or each value) Table 1: Displacement and speed of cart at different times Time (s)Displacement (m)Speed 1.02.42.4 m/s 2.14.92.3 m/s 3.17.62.2 cm/s

38. 38 Graph Title or description Labels  Independent variable on horizontal axis  Dependent variable on vertical axis Units Scales  Horizontal and vertical can be different

39. 39 Graph Example

40. 40 Linear Relationship m: slope b: y-intercept x y x1x1 x2x2 y1y1 y2y2 b Direct Relationship:

41. 41 Inverse Relationship Hyperbola