Unit I Units and Measurement

1. Objectives- Express lengths, mass, time in SI units. - Convert distances between different units. - Describe time intervals in hours, minutes, and seconds. - Convert time in mixed units to time in seconds. - Describe the mass of objects in grams and kilograms. Unit I Units and Measurement

2. It All Starts with a Ruler!!!

3. I. Two Systems of Units • Metric system and International System of Units • meter • kilogram • second • Kelvin • 2. English system • inches, feet, yards, and miles. • pound • Fahrenheit

4. 3. SI units meter (m): unit of length kilogram (kg): unit of mass second (s): unit of time

5. meter, (SI unit symbol: m), is the fundamental unit of length in the International System of Units (SI). Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level). Since 1983, it has been defined as "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second." National Prototype Metre Bar ( alloy of ninety percentplatinum and ten percent iridium) in  International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, France.

6. kilogramme ( kg), is the base unit of mass in the International System of Units (SI) Is defined as being equal to the mass of the International Prototype of the Kilogram (platinum–iridium alloy) in International Bureau of Weights and Measures in Sèvres, France

7. Second (sec or s) The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

8. UNITS (Systéme Internationale)

9. 4. Examples The units for length, mass, and time (as well as a few others), are regarded as baseSI units. These units are used in combination to define additional units for other important physical quantities such as force andenergy.

10. II THE CONVERSION OF UNITSA) relation between different units 1 ft = 0.3048 m 1 mi = 1.609 km 1 liter = 10-3 m3

11. Example 1.1 Grandma traveled 27 minutes at 44 m/s. How many miles did Grandma travel? mile/min=1.64mile/min 44.3 miles

12. B) How to convert Example 1The World’s Highest Waterfall The highest waterfall in the world is Angel Falls in Venezuela, with a total drop of 979.0 m. Express this drop in feet. Since 3.281 feet = 1 meter, it follows that (3.281 feet)/(1 meter) = 1 and (1 meter) / (3.281 feet)=1 For meter  feet:

13. Convert 100km to miles • A football field is 100 yards long. • What is this distance expressed in meters?

14. C) unit convert chart

16. D) Summary Reasoning Strategy: Converting Between Units 1. In all calculations, write down the units explicitly. 2. Treat all units as algebraic quantities. When identical units are divided, they are eliminated algebraically. 3. Use the conversion factors in reference tables. Be guided by the fact that multiplying or dividing an equation by a factor of 1 does not alter the equation.

17. time • Two ways to think about time: • What time is it? • 3 P.M. Eastern Time on April 21, 2004, • How much time has passed? • 3 hr: 44 min: 25 sec. • A quantity of time is often called a time interval.

18. Converting Mixed Units • You are asked for time in seconds. • You are given a time interval in mixed units. 1 hour = 3,600 sec 1 minute = 60 sec • Do the conversion: 1 hour = 3,600 sec 26 minutes = 26 × 60 = 1,560 sec • Add all the seconds: t = 3,600 + 1,560 + 31.25 = 5,191.25 sec

19. Time Units

20. E) Practice Example 2Interstate Speed Limit Express the speed limit of 65 miles/hour in terms of meters/second. Use 5280 feet = 1 mile and 3600 seconds = 1 hour and 3.281 feet = 1 meter.

21. More practice • 1. Convert 789 cm2 to m2 1m=100cm, 1m2=100cm *100cm=10000cm2 =0.0789 2. Convert 75.00 km/h to m/s 75.00 km x 1000 m x 1 h___ = 20.83m/s h 1 km 3600 s

22. III Limits of Measurement • A). Accuracy and Precision

23. Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

24. Example: Accuracy • Who is more accurate when measuring a book that has a true length of 17.0cm? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

25. Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

26. Example: Precision Who is more precise when measuring the same 17.0cm book? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

27. Example: Evaluate whether the following are precise, accurate or both. Accurate Not Precise Not Accurate Precise Accurate Precise

28. --Why significant figures is important?--What does significant figures in a number consist of?--How to record measurement with proper significant figures? (digram)--List the rules in counting significant figures (zero rules)--Rules in calculation: Multiplication rule Division rule Addition & subtraction rule Rule in calculate average

29. B) Significant Figures • The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.

30. Centimeters and Millimeters 40.16 cm

31. The length of this miniature piezo electric motor is: 8.0 mm

32. B.1) Finding the Number of Sig Figs: • All non-zero digits are significant. • Zeros between two non-zero digits are significant. • Leading zeros are not significant. • Trailing zeros in a number containing a decimal point are significant. • trailing zeros in a number not containing a decimal point can be ambiguous. (scientific notation is the solution)

33. One convention about trailing zero A barplaced over ( or under) the last significant figure; any trailing zeros following this are insignificant Example: 500 has 1 s.f. 5 500 has 2 s.f. 500. has 3 s.f.

34. Scientific notation Write number in form:

35. How many sig figs? 7 2 3 5 1 10302.00 100.00 970 0.001 0.00250 10302 1.0302x104 2 5 1 5

36. B.2)Sig Figs in Addition/Subtraction Express the result with the same number of decimal places as the number in the operation with the least decimal places. Ex: 2.33 cm + 3.0 cm 5.3 cm (Result is rounded to one decimal place)

37. B.3) Sig Figs in Multiplication/Division • Express the answer with the same sig figs as the factor with the least sig figs. • Ex: 3.22 cm x 2.0 cm 6.4 cm2(Result is rounded to two sig figs)

38. More example • 2330 cm • + 3.0 cm • 2330 cm

39. B.4) Constant and Counting Numbers • Constant number have infinite sig. figs. • Counting numbers have infinite sig figs. • Ex: 3 apples • Eg. π=3.1415926……

40. C) practice 1.Calculate Volume of sphere with 2. Perimeter of the big circle

41. Try the following 7.895 + 3.4= (8.71 x 0.0301)/0.056 = 13m = A= = 4.91m2

42. IV Dimension Analysis – some simple rules 1.In : The product unit is the product of the individual unit of each of those variables. (Ditto for ratios.) 2. : Different terms can only added together in a sum if each term in the sum has the same unit type. (Ditto for subtraction.)

43. Example 1 - impossible: 40m + 20m/s or 12.5 s - 20m2 - Can Do: 50.0m + 20.55m=70.6m and 40m/s +11m/s =51m/s - Can Do, but need to convert into same unit: 40m + 11cm = 40m + 11cm = 40.11m

44. Example 2 The above expression yields: 4.5 m kg 4.5 g km A or B Impossible to evaluate (dimensionally invalid)

45. IV Scalars and Vectors Definition A scalar quantity is one that can be described by a single number: temperature, speed, mass A vector quantity deals inherently with both magnitude and direction: velocity, force, displacement

46. 2. Graph a Vector Arrows are used to represent vectors. The direction of the arrow gives the direction of the vector. By convention, the length of a vector arrow is proportional to the magnitude of the vector. 8 lb 4 lb

48. 3. Vector Addition and Subtraction Often it is necessary to add one vector to another. A)

49. example 1 3 m 5 m 8 m

50. B) Example 2