1. Introduction to Measurement & Vectors
MIT C.P. PHYSICS
Introduction to Measurement & Vectors

2. Science is based on measurements.

3. All measurements have:
Units

4. Length
Foot = Length of Hercules’s Foot
Mile = 1000 Soldiers’ Paces

6. 1790

7. SI Units Quantity Base Unit Symbol Length Meter m Mass Kilogram kg
Volume
Liter l
Temperature
Kelvin K
Time
Second s

8. Light travels in a vacuum during 1/299,792,458 of a second
Meter
1 Meter
Light travels in a vacuum during 1/299,792,458 of a second

9. Kilogram

10. A US cent weighs exactly 2.5 g, while the nickel weighs exactly 5 g.
2.5 grams
5.0 grams

11. Volume occupied by 1 kilogram of H2O
Liter
1 Liter
Volume occupied by 1 kilogram of H2O

12. All measurements have:
Units
Magnitude

13. Metric Prefixes
Nano is derived from dwarf in Greek. Nano is a prefix meaning (1 Nano-meter = 10-9 meter.) For example, 1 nanometer is approximately 100,000 times thinner than a human hair.

14. Powers of Ten

15. Powers of Ten

17. Very Large Measurements
k (kilo) means “one thousand of”
M (mega) means “one million of”
G (giga) means “one billion of”

18. Very Small Measurements
c (centi) means “a hundredth of”
m (milli) means “a thousandth of”
n (nano) means “a billionth of”

19. What is a “Nanometer”?
A nanometer is to one inch as one inch is to 400 miles. Another way to visualize the size: the diameter of a quarter compared to the driving distance between Los Angeles and San Francisco. One nanometer equals a billionth of a meter.

20. What is “Nanotechnology”?
The fundamental definition of Nanotechnology is that in a microenvironment that is within the dimension of one nanometer, the ability of man to understand and change nature shall be elevated to the atomic and molecular level Nanotechnology is a highly interdisciplinary field encompassing elements of colloidal science, physics, chemistry and biology.

21. Ceramic “Nano” Pores

22. How Small Am I? DNA Molecule Bacterium Red Blood Cell Carbon Buckyball
Strand of Human Hair
Red Blood Cell

23. How Small Am I? Strand of Human Hair 60,000 nanometers Bacterium
Red Blood Cell
7,000 nanometers
DNA Molecule
2 nanometers
Carbon Buckyball (C60)
1 nanometer

24. How Many Nanometers?

25. Scientific notation is used to express very large or small numbers.
10,300,000,000,000,000,000,000 carbon atoms
A carbon atom’s mass = 0.000,000,000,000,000,000,000,020 grams

26. Scientific Notation
Scientific notation consists of a coefficient multiplied by 10 raised to an exponent.
10,300,000,000,000,000,000,000 = 1.03 x 10^22 = 1.03 E22
0.000,000,000,000,000,000,000,020 = 2.0 x 10^-23 = 2.0 E-23

27. All measurements have:
Magnitude
Units
Uncertainty

28. Which One?
Shooter 1
Shooter 2

29. Accuracy & Precision Accurate Precise
Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured.
Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

30. Lab: How Heavy is Papa Smurf

31. Lab: How Heavy is Papa Smurf
Data Chart
Mass
(g)
Displacement
(cm)

32. Percent Error
Observed Value-Accepted Value/Accepted Value x 100%

33. Sample Problem
You complete a lab and you measured a force to be 90 Newtons. You should have measured 130 Newtons. What is your % error?
Step 1:
Observed – Accepted (Absolute Value) 40
Step 2:
Error/Accepted
0.308
Step 3:
Answer X 100%
30.8%

35. Significant Figures

36. Significant Figures

37. The numbers 1,2,3,4,5,6,7,8,9 are always significant!
Significant Figures
The numbers 1,2,3,4,5,6,7,8,9 are always significant!
Rules for “0”
Rule #1: Zeros between numbers are significant!
506
3 Significant Figures
10050
4 Significant Figures

38. Significant Figures Rule #2:
Zeros to the right of a number are NOT significant unless the are to the left of a decimal point!
4830
3 Significant Figures
4830.
4 Significant Figures

39. Significant Figures Rule #3:
Zeros to the right of a number & to the right of a decimal point are significant!
8.0
2 Significant Figures
16.40
4 Significant Figures

40. Significant Figures Rule #4:
Zeros by themselves to the left or right of a decimal point are NOT significant!
0.06
1 Significant Figure
0.008
1 Significant Figure

41. Math with Significant Figures
Multiply or divide as you normally would!
Your answer can only have as many “Sig Fig’s” as the number with the fewest significant figures!
2, X 3,200 =
641440
Since 3,200 has only 2 “Sig Figs”
640,000

42. Power of the Graph! Chart Graph Organizes Data ☺ ☺ Displays Data ☺ ☺
Predicts Data ☺

43. Power of the Graph!

44. Power of the Graph!

45. Lab: Mr. G’s Cup Challenge

46. Lab: Mr. G’s Cup Challenge

47. Lab: Mr. G’s Cup Challenge

48. Lab: Mr. G’s Cup Challenge
Data Chart
Trial
Setting
Distance (cm) 1 2 3
Average 4

49. Proportional Relationships
Direct Proportion
Indirect Proportion

50. Vectors

51. Function of Vectors
Magnitude
Direction

52. Vector Interpretation
Magnitude
Scale:
1 cm = 50 km/hr
Direction

53. Vector Interpretation

54. Vector Addition

56. Vector Addition

57. Lab: Vector Addition (Force Table)

58. Lab: Vector Addition ( Force Table)
Each notch on the table = 10°
Always have the ring over the hole
Always have Vector A = 0 °

59. Lab: Vector Addition ( Force Table)
Vector B
Resultant Vector
Trial #
Force (N)
Angle (°) 1 2 3 4 5 6 7 8 9 10

60. Vector Addition
Head-to-Tail Method

61. Vector Addition
Head-to-Tail Method

62. Vector Addition
Head-to-Tail Method
Step 1:
Step 2:

63. Vector Addition
Head-to-Tail Method

64. Vector Addition
Head-to-Tail Method

65. Lab: Validating Force Table Lab

66. Lab: Validating Force Table Lab
Observed Resultant
Calculated Resultant
Trial #
Force
(N)
Angle
(°) 1 2 3 4 5 6 7 8 9 10

67. Vector Addition
Graphical Method

68. Vector Addition
Graphical Method

69. Lab: Interactive Vector Addition

70. Lab: Interactive Vector Addition
Resultant Vector
Trial x y 1 2 3 4 5 6 7 8 9 10

71. Vector Addition
Pythagorean Method

72. Vector Addition Pythagorean Method Step 1: Determine the Magnitude
R = 15.6 N

73. Vector Addition Pythagorean Method Step 1: Determine the Direction
Sin Θ = b/c
Sin Θ = 11/15.6
Sin Θ =
Θ = 45°

74. Friction Force that opposes motion.
Resistance caused by 2 objects in contact with each other.

76. Increasing Friction
Make surfaces rougher!

77. Increasing Friction
Make surfaces wider!

78. Increasing Friction
Increase weight!

79. High Friction

80. Low Friction

81. Lubricant

82. Friction between 2 nonmoving objects.
Static Friction
Friction between 2 nonmoving objects.

83. Static Friction

84. Coefficient Determination
µ static = tan (angle of tilt) 

85. Lab: Coefficient of Static Friction

86. Lab: Coefficient of Static Friction
Data Chart
Footwear
Type
Angle of Elevation
Coefficient of Static Friction

87. Sliding Friction
Kinetic Friction

88. Friction between moving object(s).
Sliding Friction
Friction between moving object(s).

89. Sliding Friction

90. Coefficient Determination
µ kinetic = Force/Normal
A block of wood is shown sliding across a wooden table. Notice that the force of kinetic friction (fk) is equal to 40% of the normal force (FN).   The coefficient of kinetic friction would be 0.4. 

91. Coefficient Determination
µ kinetic = Force/Normal
As we compare the simulation of wood on wood to wood on asphalt, we find that the amount of friction on the block increased for the same amount of weight. The coefficient of kinetic friction would be 0.6! 

92. Comparing Coefficients
µ kinetic = Force/Normal

93. Lab: Coefficient of Sliding Friction

94. Lab: Coefficient of Sliding Friction
Data Chart
Surface
Type
F(gravity)
(N)
F(applied)
Coefficient
Of Sliding Friction
Plastic
Sandpaper
Cardboard
Wood

95. Comparing Coefficients
Coefficient of Friction
Surfaces
Static Friction
Kinetic Friction
Steel on steel (dry)
0.6
0.4
Steel on steel (greasy)
0.1
0.05
Teflon on steel
0.041
0.04
Brake lining on cast iron
0.3
Rubber tires on dry pavement
0.9
0.8
Metal on ice
0.022
0.02