PHY 2048 Summer 2010

1. PHY 2048 Summer 2010 LECTURE 1 Measurements

2. POWERS OF TEN 1 10 100 1,000 10,000 100,000 1,000,000 = 101 = 102 = 103 = 104 = 105 = 106 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 104 310,000,000,000 = 3.1 x 1011 0.001000 = 1.0 x 10-3 0.0000000000012 = 1.2 x 10 -12

4. What number is 510-5107 • 5 • 0.5 • 50 • 500 • None of the above

5. 500 x 6000 = (5x102) x (6x103) = 30 x 105 = 3x106 6000 ÷ 500 = (6 x 103) ÷ (5x102) = 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) = 0.5x103 = 5x102 =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 miles per hour miles pounds 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.

7. TheBritish System of Measurementis 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. 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 centimeter = 10 millimeters

9. Relation betweenSIandBritishsystems metric British approximate relation m yd 1 yd = 0.9 m m mile 1 mile = 1600 m mm in 1 in = 25 mm 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 (abbreviatedSIfrom SystèmeInternationale) Quantity unit symbol Length meter m Time second s Mass kilogram Kg The meter, second, and kilogram are called base units in SI Other units are expressed in terms of them

14. Common prefixes in SI Prefixes are standard letters that are attached in front of a unit and make it a multiple of some power of 10. the prefix is read and multiplies the unit by μ micro 10-6 m milli 10-3 c centi 10-2 K kilo 103 M mega 106 G giga 109

15. Common Prefixes

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 Quantity unit symbol Length meter m

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

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

22. International System of Units (abbreviatedSIfrom SystèmeInternationale) Quantity unit symbol Length meter m Time second s Mass kilogram Kg 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

24. If a distanced has units ofmeters, and a timeT has units ofseconds, does the quantityT + dmake sense physically? What about the quantityd/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?(a) v = at, (b) v = ½ at2 (c) t = a/v, (d) v2 = 2ax

27. To find a speed requiresmeasurements oflengthandtime.

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

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

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

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) acceleration = ______________________ 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 Quantity unit symbol Length meter m Time second s Mass kilogram Kg Speed meter/sec m/s Acceleration meter/sec2 m/s2

40. Here two heavy balls begin “free fall” at the same time. 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.

41. A Vector and Its Scalar Components The vector ŕ is defined by its length (1.50m) and its direction angle(25o) 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, rx=1.36m, and its Y component, ry=0.634m.

43. A Vector Whose x and y Components Are Positive

44. Vector Angle

45. Vector Angle

46. Adding Several Vectors

47. Identical Vectors A at Different Locations

48. A + B = B + A

49. A + B = B + A

50. Graphical Addition of Vectors