Download Notes with questions - Department of Physics and Astronomy

HONORS 227
1 September 2015
Dr. Harold Geller
College of Science
School of Physics, Astronomy and Computational Sciences
George Mason University
1
Chapters 1 and 2 and
Other Stuff
• A Personal Response System
(iClickers)
• Units of length, mass and time
• Metric Prefixes
• Chapter 2 and the Ordered
Universe
2
iClicker Qustion
The pyramids were built by
extraterrestrials from outer space.
• A Agree
• B Disagree
3
iClicker Qustion
The location of the stars and planets at
birth determine your personality.
• A Agree
• B Disagree
4
iClicker Qustion
• Humans have never stepped foot on the
Moon’s surface.
• A Agree
• B Disagree
5
• The basic unit of angular measure is the degree (°).
6
Angular Measurements
• Subdivide one degree into 60 arcminutes
– minutes of arc
– abbreviated as 60 arcmin or 60´
• Subdivide one arcminute into 60
arcseconds
– seconds of arc
– abbreviated as 60 arcsec or 60”
1° = 60 arcmin = 60´
1´ = 60 arcsec = 60”
7
iClicker Question
• How many arcseconds are there in a
degree?
A 60 arcseconds
B 360 arcseconds
C 3600 arcseconds
D 600 arcseconds
E These are incompatible units.
8
Powers-of-ten notation is a useful
shorthand system for writing numbers
9
iClicker Question
Which measurement of an average
classroom door is closest to 2 meters?
• A. Thickness
• B. Width
• C. Height
• D. Surface area
• E. Volume
10
iClicker Question
• What is the result if you multiply 1015
by 1010?
A 1015
B 1010
C 10150
D 1025
E 2 x 1015
11
iClicker Question
• What is the result if you add 1015 to
1015?
A 1015
B 1030
C 10150
D 1025
E 2 x 1015
12
iClicker Question
• What is the result if you multiply 1015
by 1015?
A 1015
B 1030
C 10150
D 10225
E 2 x 1015
13
Common Prefixes for Powers of Ten
Factor
(billion)
109
(million)
106
(thousand)
103
(hundredth)
10-2
(thousandth)
10-3
(millionth)
10-6
(billionth)
10-9
Name
Symbol
Giga-
G
Mega-
M
kilo-
k
centi-
c
milli-
m
micro-

nano-
n
14
Astronomical distances are often measured
in astronomical units, lightyears or parsecs
• Astronomical Unit (AU)
– One AU is the average distance between Earth and
the Sun
– 1.496 X 108 km or 92.96 million miles
• Light Year (ly)
– One ly is the distance light can travel in one year
at a speed of about 3 x 105 km/s or 186,000
miles/s
– 9.46 X 1012 km or 63,240 AU
• Parsec (pc)
– the distance at which 1 AU subtends an angle of 1
arcsec or the distance from which Earth would
appear to be one arcsecond from the Sun
– 1 pc = 3.09 × 1013 km = 3.26 ly
15
iClicker Question
• Which unit of the following is the
largest?
A Kilometer
B Astronomical Unit (AU)
C Light Year (ly)
D Parsec (pc)
E Gigameter
16
Science is an adventure of
the human mind
17
HNRS 227
Chapter 2 – Ordered Universe
18
Main Concepts I will focus Upon
from Chapter 2
•
•
•
•
•
•
•
•
Speed vs. Velocity
Acceleration
Force
Falling Objects
Newton’s Laws of Motion
Momentum
Angular Momentum
Universal Law of Gravity
19
Speed and Velocity
• Speed
– distance traveled in a unit of time
– a scalar quantity
• Velocity
– speed and direction
– a vector quantity
20
iClicker Question
• What is the difference between speed
and velocity?
A
Speed is a vector and velocity is
a scalar quantity.
B
Speed is a scalar and velocity is
a vector quantity.
C
There is no difference between
speed and velocity.
D
All of the above are true
statements.
21
Questions for Thought
• What is acceleration?
A The change in distance per
change in time.
B The change in position per
unit of time.
C The ratio of the change in
velocity per change in time.
D The change of time per unit
of length.
22
Questions for Thought
• An insect inside a bus flies from the back toward the
front at 5.0 miles/hour. The bus is moving in a
straight line at 50 miles/hour. What is the speed of
the insect?
A
The speed of the insect is 5 miles
per hour relative to the bus.
B
The speed of the insect is 55
miles per hour relative to the ground.
C
The speed of the insect is 50 miles per
hour relative to the ground.
D
Both A and B above are true.
E
A, B and C above are true.
23
Force
• Definition of force
– something that causes a change in the
motion of an object
• a push or pull
• an electric, magnetic, gravitational effect
• a vector quantity
• Net force - Resultant Force
24
Inertia
• Defining Inertia
– tendency of an object to remain in its
current state of motion
• the more massive the more inertia
• think of stopping a car vs. truck
25
Acceleration Due to Gravity
• Direction of acceleration due to gravity
– directed to center of Earth
• Think: scalar or vector?
– a vector quantity
• Why?
– has magnitude and direction
26
Generalized Motion
• Motion can be viewed as a combination
of movements
– vertical component
• typically gravitational acceleration
– horizontal component
• some force from muscle, gunpowder, etc.
27
Question for Thought
• What happens to the velocity and
acceleration of an object in free fall?
A The velocity decreases as the acceleration
remains the same.
B The velocity increases as the acceleration
remains the same.
C The velocity increases and the
acceleration decreases.
D The velocity increases and the
acceleration increases.
E Both velocity and acceleration decrease.
28
Question for Thought
• In the equation d=1/2*a*t2, if a is 9.8
meters per second per second and t is in
seconds, what is the unit of d?
A seconds
B meters
C kilometers
D feet per second
E meters per second
29
Question for Thought
• Do you recall what inertia is?
• Inertia is the property of matter that
an object will remain in unchanging
motion or at rest in the absence of an
unbalanced force.
30
Question for Thought
• Where does the unit s2 (or concept of
“square second”) come from?
• Acceleration is change in velocity per change in time,
with units of (m/s)/s. When the fraction is
simplified, you get meters per second squared. The
“seconds squared” indicates that something that
changes in time is changing in time, that is, the ratio
of change in distance per unit of time is changing in
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time.
Question for Thought
• Neglecting air resistance, what are the
forces acting on a bullet after it has
left the barrel of a rifle?
–A
–B
–C
–D
The force of air acting up and
gravity acting down.
Only the force of gravity acting
straight down.
There are no forces acting at this
point.
All of the above are true.
32
Question for Thought
• How does the force of gravity on a ball
change as a ball is thrown straight up in the
air?
A The force of gravity increases.
B The force of gravity decreases.
C The force of gravity remains the same.
D The force of gravity increases then
decreases.
E The force of gravity decreases then
increases.
33
Sample Question
• An object falls from a bridge and hits
the water 2.5 seconds later.
– A) With what velocity did it strike the
water?
– B) What is the average velocity during the
fall?
– C) How high is the bridge?
34
Sample Answer
23. These three questions are easily answered by using the three sets of relationships, or
equations, that were presented in this chapter:
(a)
vf
vf
(b)
v
(c)
v
 at  vi
m
 m
 9.8 2 

2.50
s


0
s 
s
m
 9.8  2.50 2  s
s
 25 m / s

vf  vi
2

25 m / s  0
2
 13
m
s
d
 d  vt
t
 m
d  13 
2.50 s
s 

 13  2.50
 33 m
m
s
s
35
Newton’s Laws of Motion
• Newton’s First Law of Motion
– body at rest tends to stay at rest and body
in uniform motion will stay in straight line
uniform motion unless acted upon by an
outside force
• Newton’s Second Law of Motion
– the acceleration of a body is proportional
to the force being applied
–F = m*a
36
Newton’s Laws of Motion
• Newton’s Third Law of Motion
– for every force there is an equal and
opposite force (action and reaction)
37
Question for Thought
• How can there ever be an unbalanced
force on an object if every action has an
equal and opposite reaction?
• The action and reaction forces are between
two objects that are interacting. An
unbalanced force occurs on a single object as
the result of one or more interactions with
38
other objects.
Sample Question
• What force would an asphalt road have
to be to give a 6,000 kilogram truck in
order to accelerate it at 2.2 meters per
second per second?
39
Sample Question Answer
2.
F = ma
m
F  6,000 kg  2.2 2  1.3  104 N
s
40
Momentum
• By definition momentum is the product
of
–
mass and velocity
• Conservation of momentum
–total momentum of a closed
system remains constant
41
Question for Thought
• Is it possible for a small car to have the
same momentum as a large truck?
–A
–B
Yes
No
• Yes, the small car would have to be moving with a
much higher velocity, but it can have the same
momentum since momentum is mass times velocity.
42
Angular Momentum
• Torque
– Twisting force
• Conservation of Angular Momentum
– “an object that is rotating will keep
rotating unless a twisting force called a
torque acts to make it stop”
– Applications include
• Ice skater
• Inertial guidance systems
43
Universal Law of Gravity
• Newton’s Universal Law of Gravitational
Attraction
– every object is attracted to every other
object
– the force is proportional to masses and
inversely proportional to the distance
squared
»F = (G*m*M) / r2
44
A Problem of Very Little
Attraction
• What is the gravitational force between
two 100 kilogram people separated by 1
meter?
45
Really just a little
Use the formula for the force of gravity:
F = G*m*M / r2
where G = 6.67 x 10-11 Nm2/kg2
and m = 100 kg
and M = 100 kg
and r = 1
=======================
Then
F = 6.67 x 10-11 Nm2/kg2 *100 kg*100 kg / (1 meter) 2
F = 6.67 x 10-7 N
46