1. PHY 2048
Fall 2009
LECTURE 1
Units & Calculations

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
= 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
= 1.0 x 10-3
= 1.2 x

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 = (5x10-3) x (6x10-6) =
30x10-9=3x10-8
0.003 ÷ = (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:
How far:
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. 1 mile = 1760 yards 1 yard = 3 feet 1 foot = 12 inches
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. 1 centimeter = 10 millimeters
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 between SI and British systems
metric British approximate relation
m yd yd = 0.9 m
m mile mile = 1600 m
mm in in = 25 mm
liter quart quart = 1 liter
liter gallon gallon = 3.8 liters
g lb lb = 450 g

10. 1 lb on earth has a mass of 0.45 kg
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)
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
m milli
c centi
K kilo
M mega
G giga

15. Common Prefixes Power Prefix Abbreviation 1015 peta P 1012 tera T 109
giga G
106
mega M
103
kilo k
102
hecto h
101
deka da
10–1
deci d
10–2
centi c
10–3
milli m
10–6
micro
10–9
nano n
10–12
pico p
10–15
femto f

16. Mass is the quantity of matter in an object
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.
Demo with hammer+lead+wood here.

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
(abbreviated SI from Système Internationale)
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
Quantity
Dimension
Distance
[L]
Area
[L2]
Volume
[L3]
Velocity
[L]/[T]
Acceleration
[L]/[T2]
Energy
[M][L2]/[T2]

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 at2 (c) t = a/v, (d) v2 = 2ax

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

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.
ANIMATED: one mouse click brings up the last sentence.
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. (final speed – initial speed)
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.
ANIMATED: One mouse clicks bring the last paragraph in.

35. A tennis ball and a golf ball dropped side-by-side in air
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…
Tennis ball and golf ball falling side-by-side in air; the tennis ball lags.

36. Skydivers depend on air to retard their downward acceleration.
Terminal speed in this position average 120 mph (about 50 m/s).
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.
Notice here that the vacuum is only partial, point out the top and bottom images and show that the feather is being left behind…

38. In a vacuum the feather and apple would fall exactly together if released at the same time. The positions here simulate a strobe photo.

39. International System of Units
Quantity unit symbol
Length meter m
Time second s
Mass kilogram Kg
Speed meter/sec m/s
Acceleration meter/sec 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.
ANIMATED: Two mouse clicks. (The next two slides appear with a mouse click with almost the same figure but different text, making this one seem animated.)

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

51. Component Addition of Vectors

52. Component Addition of Vectors

53. Vector Subtraction

54. Vector Subtraction
D= A – B
Dx= Ax – Bx
Dy= Ay - By

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