1. PHY 2048 Summer 2010 LECTURE 1 Measurements

2. POWERS OF TEN 1 10 100 1,000 10,000 100,000 1,000,000 = 10 1 = 10 2 = 10 3 = 10 4 = 10 5 = 10 6 1 0.1 0.01 0.001 0.0001 0.00001 0.000001 = 10 -1 = 10 -2 = 10 -3 = 10 -4 = 10 -5 = 10 -6

3. Wright the following numbers in scientific notation: 45100 = 4.5 x 10 4 310,000,000,000 = 3.1 x 10 11 0.001000 = 1.0 x 10 -3 0.0000000000012 = 1.2 x 10 -12

4. What number is 5  10 -5  10 7 A.5 B.0.5 C.50 D.500 E.None of the above

5. 500 x 6000 = (5x10 2 ) x (6x10 3 ) = 30 x 10 5 = 3x10 6 6000 ÷ 500 = (6 x 10 3 ) ÷ (5x10 2 ) = 60 ÷ 5 =12 0.005 x 0.000006 = (5x10 -3 ) x (6x10 -6 ) = 30x10 -9 =3x10 -8 0.003 ÷ 0.000006 = (3x10 -3 ) ÷ (6x10 -6 ) = 0.5x10 3 = 5x10 2 =500

6. There are questions like "how fast", "how far", or "how much" which, when answered, we must supply a unit of measurement: How fast: 50 How far: 30 How much: 8 Because of this, numbers in science will always have "units". These units are just as important as the numbers when communicating observations. Never write a number without its units. miles per hour miles pounds

7. Theis commonly used as the day to day system in the United States. We are familiar with this system: we know about pounds, feet, and gallons. However, the British system is an impossible system to do conversions between units since the relations between units have no pattern (they are arbitrary). The British System of Measurement is commonly used as the day to day system in the United States. We are familiar with this system: we know about pounds, feet, and gallons. However, the British system is an impossible system to do conversions between units since the relations between units have no pattern (they are arbitrary). 1 mile = 1760 yards 1 yard = 3 feet 1 foot = 12 inches

8. Theof measurement (abbreviated SI) is commonly called the metric system in the United States. The relation between units are multiples of ten. The International System of measurement (abbreviated SI) is commonly called the metric system in the United States. The relation between units are multiples of ten. All science measurements are made using this system. 1 kilometer = 1000 meters 1 meter = 100 centimeters 1 meter = 100 centimeters 1 centimeter = 10 millimeters 1 centimeter = 10 millimeters

9. Relation between SI and British Relation between SI and British systems m yd 1 yd = 0.9 m m mile 1 mile = 1600 m mm in 1 in = 25 mm metric British approximate relation liter quart 1 quart = 1 liter liter gallon 1 gallon = 3.8 liters g lb 1 lb = 450 g

10. 1 meter = 3.3 ft = 39 inches 1 cm = 0.39 inches 1km = 0.62 miles 1 ft = 30 cm 1 inch = 2.5 cm 1 mile = 1.6 km 1 kg weights 2.2 lb on earth 1 lb on earth has a mass of 0.45 kg Celsius temperature =5 x (Fahrenheit temperature – 32) / 9 Fahrenheit temperature = 32 + (9 x Celsius temperature) / 5

11. Using wrong units caused trouble as recently as September 1999, when a probe launched by NASA was lost in the atmosphere of Mars because the engineers who built the engines were working in British units and the scientists who were controlling the engines were working in SI units. This lets us emphasize that units are part of every result.

12. In physics, there are three basic quantities that are the basis for everything: Length, Time, Mass We understand all these quantities from experience but we find very hard to define!

13. International System of Units ( abbreviated SI from Système Internationale) Length meter m Time second s Mass kilogram Kg Quantity unit symbol The meter, second, and kilogram are called base units in SI Other units are expressed in terms of them

14. Common prefixes in SI μ micro 10 -6 m milli 10 -3 c centi 10 -2 the prefix is read and multiplies the unit by K kilo 10 3 M mega 10 6 G giga 10 9 Prefixes are standard letters that are attached in front of a unit and make it a multiple of some power of 10.

15. Common Prefixes 10 15 petaP 10 12 teraT 10 9 gigaG 10 6 megaM 10 3 kilok 10 2 hectoh 10 1 dekada 10 –1 decid 10 –2 centic 10 –3 millim 10 –6 microm 10 –9 nanon 10 –12 picop 10 –15 femtof PowerPrefixAbbreviation

16. Mass is the quantity of matter in an object. It is also the measure of the inertia that an object exhibits in response to any effort made to start it, stop it, or change its state of motion in any way.

17. To compare the inertia, or mass, of two objects, accelerate them side-by-side. The one that requires the most force is the one with the larger mass.

18. International System of Units Quantity unit symbol

19. International System of Units Length meter m Quantity unit symbol

20. International System of Units Length meter m Time second s Quantity unit symbol

21. International System of Units Length meter m Time second s Mass kilogram Kg Quantity unit symbol

22. International System of Units ( abbreviated SI from Système Internationale) Length meter m Time second s Mass kilogram Kg Quantity unit symbol The meter, second, and kilogram are called base units in SI Other units are expressed in terms of them

23. Dimensions of Some Common Physical Quantities Distance[L] Area[L 2 ] Volume[L 3 ] Velocity[L]/[T] Acceleration[L]/[T 2 ] Energy[M][L 2 ]/[T 2 ] QuantityDimension

24. If a distance d has units of meters, and a time T has units of seconds, does the quantity T + d make sense physically? What about the quantity d/T ?

25. The quantity T + d does not make sense physically, because it adds together variables that have different physical dimensions. The quantity d / T does make sense, however; it could represent the distance d traveled by an object in the time T.

26. Which of the following equations is dimensionally consistent? Which of the following equations is dimensionally consistent? (a) v = at, (b) v = ½ at 2 (c) t = a/v, (d) v 2 = 2ax

27. To find a speed requires measurements of length and time. of length and time.

28. Average speed is distance traveled divided by the time used. average speed = distance/time average speed = distance/time v = d/t

29. What is the unit of speed in SI? Speed=length/time Quantity unit symbol

30. International System of Units Length meter m Time second s Mass kilogram Kg Speed meter/sec m/s Quantity unit symbol

31. Photographs can be used to measure motion. While the camera’s shutter was open, both the runners and the camera moved to blur this photo.

32. The real speed at any moment is called instantaneous speed.

33. Galileo was the first to analyze motion in terms of measurements and mathematics. He described acceleration, which is the rate of change of speed. (final speed – initial speed) (final speed – initial speed) acceleration = ______________________ time required time required

34. Galileo did experiments to convince others that the acceleration caused by gravity would be the same for all freely falling objects if there was no air to retard their motion. He dropped two heavy metal balls together from the leaning tower in Pisa, Italy. Although one weighed far more than the other, they reached the ground almost at the same time.

35. A tennis ball and a golf ball dropped side-by-side in air. The tennis ball is affected more by the air’s resistance than the golf ball. The larger the object is, and the faster it is falling, the greater the air’s resistance to its motion, as skydivers all know…

36. Skydivers depend on air to retard their downward acceleration.

37. When most of the air is removed from a container, feathers and apples fall almost side- by-side, their speeds changing at almost the same rate. If all the air were removed, they would accelerate downward at exactly the same rate.

39. International System of Units Length meter m Time second s Mass kilogram Kg Speed meter/sec m/s Quantity unit symbol Acceleration meter/sec 2 m/s 2

40. Here two heavy balls begin “free fall” at the same time. The red one is dropped, so it moves straight downward. The red one is dropped, so it moves straight downward. The yellow ball is given some speed in the horizontal direction as it is released. The yellow ball is given some speed in the horizontal direction as it is released.

41. A Vector and Its Scalar Components The vector ŕ is defined by its length (1.50m) and its direction angle(25 o ) measured counterclockwise from the positive X axis.

42. A Vector and Its Scalar Components Alternatively, the vector ŕ can be defined by its X component, r x =1.36m, and its Y component, r y =0.634m.

43. A Vector Whose x and y Components Are Positive

44. Vector Angle

46. Adding Several Vectors

47. Identical Vectors A at Different Locations

48. A + B = B + A

50. Graphical Addition of Vectors

51. Component Addition of Vectors

53. Vector Subtraction

54. D= A – B D x = A x – B x D y = A y - B y

55. Unit Vectors The unit vectors x and ŷ points in the positive x and y directions, respectively.

56. Vector Components

57. Multiplying a Vector by a Scalar