Physics 207, Lecture 2, Jan 24 ‘08
Agenda for Today
 Finish Chapter 1, Chapter 2
 Units and scales, order of magnitude calculations, significant digits
(on your own for the most part)
 Position, Displacement
 Velocity (Average and Instantaneous), Speed
 Acceleration
 Dimensional Analysis
Assignments:
 For next class: read Chapter 3 (Vectors)
 Mastering Physics: HW1 due Monday 6pm
 Mastering Physics: HW2 due Wednesday 6pm
(Each assignment will contain ~ 10 problems)
Physics 207: Lecture 2, Pg 2
Length
Distance
Radius of Visible Universe
To Andromeda Galaxy
To nearest star
Earth to Sun
Radius of Earth
Sears Tower
Football Field
Tall person
Thickness of paper
Wavelength of blue light
Diameter of hydrogen atom
Diameter of proton
Length (m)
1 x 1026
2 x 1022
4 x 1016
1.5 x 1011
6.4 x 106
4.5 x 102
1 x 102
2 x 100
1 x 10-4
4 x 10-7
1 x 10-10
1 x 10-15
Physics 207: Lecture 2, Pg 3
Time
Interval
Age of Universe
Age of Grand Canyon
Avg age of college student
One year
One hour
Light travel from Earth to Moon
One cycle of guitar A string
One cycle of FM radio wave
One cycle of visible light
Time for light to cross a proton
Time (s)
5 x 1017
3 x 1014
6.3 x 108
3.2 x 107
3.6 x 103
1.3 x 100
2 x 10-3
6 x 10-8
1 x 10-15
1 x 10-24
Physics 207: Lecture 2, Pg 4
Mass
Object
Mass (kg)
Visible universe
Milky Way galaxy
Sun
Earth
Boeing 747
Car
You
Dust particle
Bacterium
Proton
Electron
Neutrino
~ 1052
7 x 1041
2 x 1030
6 x 1024
4 x 105
1 x 103
7 x 101
1 x 10-9
1 x 10-15
2 x 10-27
9 x 10-31
<1 x 10-36
Physics 207: Lecture 2, Pg 5
Order of Magnitude Calculations / Estimates
Question: How many french fries, placed end to
end, would it take to reach 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
Physics 207: Lecture 2, Pg 6
Dimensional Analysis

This is a very important tool to check your work
 Provides a reality check (if dimensional analysis fails
there’s no sense in putting in the numbers; this leads to
the GIGO paradigm!)

Example
When working a problem you get the answer for distance
d = v t 2 ( velocity x time2 )
Quantity on left side = L
Quantity on right side = L / T x T2 = L x T

Left units and right units don’t match, so answer is
nonsense
Physics 207: Lecture 2, Pg 7
Lecture 2, 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)
 Note: Force has dimensions of ML/T2
Which of the following formulas for F could be correct ?

(a)
F = mvR
(b)
(c)
Physics 207: Lecture 2, Pg 8
Converting between different systems of units

Useful Conversion factors:
 1 inch
= 2.54 cm
1m
= 3.28 ft
 1 mile
= 5280 ft
 1 mile
= 1.61 km

Example: Convert miles per hour to meters per second:
Physics 207: Lecture 2, Pg 9
Lecture 2, Home Exercise 1
Converting between different systems of units

Travelling 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.)
Physics 207: Lecture 2, Pg 10
Motion in One-Dimension (Kinematics)
Position / Displacement

Position is usually measured and referenced to an origin:
10 meters
 At time= 0 seconds Joe is 10 meters to the right of the lamp
 origin = lamp
 positive direction = to the right of the lamp
 position vector :
-x
+x
10 meters
O
Joe
Physics 207: Lecture 2, Pg 11
Position / Displacement


One second later Joe is 15 meters to the right of the lamp
Displacement is just change in position.
Δx = xf - xi
15 meters
10 meters
xi
O
xf
Joe
xf = xi + Δx
Δx = xf - xi = 5 meters
Δt = tf - ti = 1 second
Physics 207: Lecture 2, Pg 12
Average speed and velocity
Changes in position vs Changes in time
•
Average velocity = total distance covered per total time,

Speed is just the magnitude of velocity.
 The “how fast” without the direction.
•
Instantaneous velocity, velocity at a given instant
Physics 207: Lecture 2, Pg 13
Average Velocity Exercise 2
What is the average velocity over the first 4 seconds ?
x (meters)
6
4
2
-2




1
2
3
4 t (seconds)
2 m/s
4 m/s
1 m/s
0 m/s
Physics 207: Lecture 2, Pg 14
Average Velocity Exercise 3
What is the average velocity in the last second (t = 3 to 4) ?
x (meters)
6
4
2
-2




1
2
3
4 t (seconds)
2 m/s
4 m/s
1 m/s
0 m/s
Physics 207: Lecture 2, Pg 15
Instantaneous velocity Exercise 4
What is the instantaneous velocity in the last second?
x (meters)
6
4
2
-2
1
2
3
4 t (seconds)
 -2



m/s
4 m/s
1 m/s
0 m/s
Physics 207: Lecture 2, Pg 16
Key point:

If the position x is known as a function of time, then
we can find both velocity v
x
t
v
t
 Area
under the v(t) curve yields the change in position
 Algebraically, a special case, if the velocity is a constant
Physics 207: Lecture 2, Pg 17
One step further…..in one dimension

If the position x is known as a function of time,
then we can find both velocity v and acceleration
a as a function of time!
x
v
a
t
t
t
Physics 207: Lecture 2, Pg 18
Lecture 2, Exercise 5
Motion in One Dimension
When throwing a ball straight up, which of the following is
true about its velocity v and its acceleration a at the highest
point in its path?
 Both
v = 0 and a = 0
 v ≠ 0, but a = 0
 v = 0, but a ≠ 0
 None of the above
y
Physics 207: Lecture 2, Pg 19