1. Why units matter! Flight 173 ran out of fuel in flight….
You may ask, “So, how does a jet run out of fuel at ft ???"
1.  A maintenance worker found that the fuel gauge did not work on ground inspection.  He incorrectly assured the pilot that the plane was certified to fly without a functioning fuel gauge if the crew checked the fuel tank levels.
2.  Crew members measured the 2 fuel tank levels at 62 cm and 64 cm.  This corresponded to 3758 L and 3924 L for a total of 7682 L according to the plane's manual.
3.  The ground crew knew that the flight required 22,300 kg of fuel.  The problem they faced was with 7,682 L of fuel on the plane, how many more liters were needed to total 22,300 kg of fuel?
4.  One crew member informed the other that the "conversion factor" (being the fuel density) was  THE CRUCIAL FAULT BEING THAT NO ONE EVER INQUIRED ABOUT THE UNITS OF THE CONVERSION FACTOR.  So it was calculated that the plane needed an additional 4,917 L of fuel for the flight. Alas, that was too little. 1

2. Lecture 2 Goals: (Highlights of Chaps. 1 & 2.1-2.4)
Conduct order of magnitude calculations,
Determine units, scales, significant digits (in discussion or on your own)
Distinguish between Position & Displacement
Define Velocity (Average and Instantaneous), Speed
Define Acceleration
Understand algebraically, through vectors, and graphically the relationships between position, velocity and acceleration
Perform Dimensional Analysis 1

3. For next class: Finish reading Ch. 2, read Chapter 3 (Vectors)
Lecture 2
Reading Assignment:
For next class: Finish reading Ch. 2, read Chapter 3 (Vectors) 1

4. Length Distance Length (m) Radius of Visible Universe 1 x 1026
To Andromeda Galaxy 2 x 1022
To nearest star 4 x 1016
Earth to Sun x 1011
Radius of Earth x 106
Sears Tower x 102
Football Field x 102
Tall person x 100
Thickness of paper x 10-4
Wavelength of blue light 4 x 10-7
Diameter of hydrogen atom 1 x 10-10
Diameter of proton x 10-15
See

5. Time Interval Time (s) Age of Universe 5 x 1017
Age of Grand Canyon x 1014
Avg age of college student x 108
One year x 107
One hour x 103
Light travel from Earth to Moon 1.3 x 100
One cycle of guitar A string x 10-3
One cycle of FM radio wave x 10-8
One cycle of visible light x 10-15
Time for light to cross a proton x 10-24

6. Mass Stuff Mass (kg) Visible universe ~ 1052 Milky Way galaxy 7 x 1041
Sun x 1030
Earth x 1024
Boeing x 105
Car x 103
Student x 101
Dust particle x 10-9
Bacterium x 10-15
Proton x 10-27
Electron x 10-31
Neutrino <1 x 10-36

7. Some Prefixes for Power of Ten
Power Prefix Abbreviation
atto a
femto f
pico p
nano n
micro m
milli m
kilo k
mega M
giga G
tera T
peta P
exa E

8. Density Every substance has a density, designated  = M/V
Dimensions of density are, units (kg/m3)
Some examples,
Substance  (103 kg/m3)
Gold
Lead
Aluminum
Water

9. What is the mass of a single carbon (C12) atom ?
Atomic Density
In dealing with macroscopic numbers of atoms (and similar small particles) we often use a convenient quantity called Avogadro’s Number, NA = x 1023 atoms per mole
Commonly used mass units in regards to elements
1. Molar Mass = mass in grams of one mole of the substance (averaging over natural isotope occurrences)
2. Atomic Mass = mass in u (a.m.u.) of one atom of a substance.
It is approximately the total number of protons and neutrons in one atom of that substance.
1u = x kg
What is the mass of a single carbon (C12) atom ?
= 2 x g/atom

10. Order of Magnitude Calculations / Estimates Question: If you were to eat one french fry per second, estimate how many years would it take you to eat a linear chain of trans-fat free french fries, placed end to end, that reach from the Earth to the moon?
Need to know something from your experience:
Average length of french fry: 3 inches or 8 cm, 0.08 m
Earth to moon distance: 250,000 miles
In meters: 1.6 x 2.5 X 105 km = 4 X 108 m
1 yr x 365 d/yr x 24 hr/d x 60 min/hr x 60 s/min = 3 x 107 sec

11. Converting between different systems of units
Useful Conversion factors:
1 inch = cm
1 m = ft
1 mile = ft
1 mile = km
Example: Convert miles per hour to meters per second:

12. Home Exercise 1 Converting between different systems of units
When on travel in Europe you rent a small car which consumes 6 liters of gasoline per 100 km. What is the MPG of the car ?
(There are 3.8 liters per gallon.)

13. Dimensional Analysis (reality check)
This is a very important tool to check your work
Provides a reality check (if dimensional analysis fails then there is no sense in putting in numbers)
Example
When working a problem you get an expression for distance
d = v t 2 ( velocity · time2 )
Quantity on left side d  L  length
(also T  time and v  m/s  L / T)
Quantity on right side = L / T x T2 = L x T
Left units and right units don’t match, so answer is nonsense

14. Exercise 1 Dimensional Analysis
The force (F) to keep an object moving in a circle can be described in terms of:
velocity (v, dimension L / T) of the object
mass (m, dimension M)
radius of the circle (R, dimension L)
Which of the following formulas for F could be correct ?
Note: Force has dimensions of ML/T2 or kg-m / s2
F = mvR
(a)
(b)
(c)

15. Note: Force has dimensions of ML/T2
Exercise 1 Dimensional Analysis Which of the following formulas for F could be correct ?
Note: Force has dimensions of ML/T2
Velocity (n, dimension L / T)
Mass (m, dimension M)
Radius of the circle (R, dimension L)
F = mvR 

16. Significant Figures
The number of digits that have merit in a measurement or calculation.
When writing a number, all non-zero digits are significant.
Zeros may or may not be significant.
those used to position the decimal point are not significant (unless followed by a decimal point)
those used to position powers of ten ordinals may or may not be significant.
In scientific notation all digits are significant
Examples:
2 1 sig fig
40 ambiguous, could be 1 or 2 sig figs
(use scientific notations)
4.0 x significant figures
significant figures
significant figures

17. Significant Figures
When multiplying or dividing, the answer should have the same number of significant figures as the least accurate of the quantities in the calculation.
When adding or subtracting, the number of digits to the right of the decimal point should equal that of the term in the sum or difference that has the smallest number of digits to the right of the decimal point.
Examples:
2 x 3.1 = 6
4.0 x 101 / 2.04 x 102 = 1.6 X 10-1
2.4 – = 2.4
See:

18. Moving between pictorial and graphical representations
Example: Initially I walk at a constant speed along a line from left to right, next smoothly slow down somewhat, then smoothly speed up, and, finally walk at the same constant speed.
Draw a pictorial representation of my motion by using a particle model showing my position at equal time increments.
2. Draw a graphical “xy” representation of my motion with time on the x-axis and position along the y-axis.
Need to develop quantitative method(s) for algebraically describing:
Position
Rate of change in position (vs. time)
Rate of change in the change of position (vs. time)

19. Tracking changes in position: VECTORS
Displacement (change in position)
Velocity (change in position with time)
Acceleration

20. Motion in One-Dimension (Kinematics) Position / Displacement
Position is usually measured and referenced to an origin:
At time= 0 seconds Pat is 10 meters to the right of the lamp
origin = lamp
positive direction = to the right of the lamp
position vector :
10 meters
Joe O -x +x
10 meters 2

21. Position / Displacement
One second later Pat is 15 meters to the right of the lamp
Displacement is just change in position
x = xf - xi
10 meters
15 meters Δx
Pat xi xf O
xf = xi + x
x = xf - xi = 5 meters to the right !
t = tf - ti = 1 second 2

22. Average Speed & Velocity Changes in position vs Changes in time
Average velocity = net distance covered per total time,
includes BOTH magnitude and direction
Speed, s, is usually just the magnitude of velocity.
The “how fast” without the direction.
Average speed references the total distance travelled
Active Figure 1

23. Representative examples of speed
Speed (m/s)
Speed of light x108
Electrons in a TV tube
Comets
Planet orbital speeds
Satellite orbital speeds
Mach
Car
Walking
Centipede
Motor proteins
Molecular diffusion in liquids

24. Instantaneous velocity Changes in position vs Changes in time
Instantaneous velocity, velocity at a given instant
If a position vs. time curve then just the slope at a point x t

25. Exercise 2 Average Velocity
x (meters) 6 4 2
t (seconds) -2 1 2 3 4
What is the magnitude of the average velocity over the first 4 seconds ?
(A) -1 m/s
(B) 4 m/s
(C) 1 m/s
(D) not enough
information to
decide.

26. Average Velocity Exercise 3 What is the average velocity in the last second (t = 3 to 4) ?
x (meters) 6 4 2 -2
t (seconds) 1 2 3 4
2 m/s
4 m/s
1 m/s
0 m/s

27. Exercise 4 Instantaneous Velocity
x (meters) 6 4 2 -2
t (seconds) 1 2 3 4
What is the instantaneous velocity at the fourth second?
(A) 4 m/s
(B) 0 m/s
(C) 1 m/s
(D) not enough
information to
decide.

28. Average Speed Exercise 5 What is the average speed over the first 4 seconds ? 0 m to -2 m to 0 m to 4 m  8 meters total
x (meters)
t (seconds) 2 6 -2 4 1 3
turning point
2 m/s
4 m/s
1 m/s
0 m/s

29. Key point: position  velocity
(1) If the position x(t) is known as a function of time, then we can find instantaneous or average velocity v x t vx t
(2) “Area” under the v(t) curve yields the change in position
A special case: If the velocity is a constant, then
x(Δt)=v Δt + x0

30. Exercise 6, (and some things are easier than they appear)
A marathon runner runs at a steady 15 km/hr. When the runner is 7.5 km from the finish, a bird begins flying from the runner to the finish at 30 km/hr. When the bird reaches the finish line, it turns around and flies back to the runner, and then turns around again, repeating these back-and-forth trips until the runner reaches the finish line.
How many kilometers does the bird fly?
Hint: Don’t focus on the bird. How many kilometers does the runner travel and how long does that take?
A. 10 km
B. 15 km
C. 20 km
D. 30 km

31. Motion in Two-Dimensions (Kinematics) Position / Displacement
Amy has a different plan (top view):
At time= 0 seconds Amy is 10 meters to the right of the lamp (East)
origin = lamp
positive x-direction = east of the lamp
position y-direction = north of the lamp N
10 meters
Amy O -x +x
10 meters 2

32. “2D” Position, Displacementy
time (sec)
position -2, , ,2 1, , ,2
(x,y meters) x
position vectors
origin
Continued on Monday….

33. Reading for Monday’s class on 9/13
Assignment Recap
Reading for Monday’s class on 9/13
Finish Chapter 2 & all of 3 (vectors) 27