Download Introduction to Modern Physics PHYX 2710

Physics of Technology
PHYS 1800
Lecture 12
Introduction
Circular Motion and
Gravitational Force
Section 0
Lecture 1
Slide 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 1
PHYSICS OF TECHNOLOGY
Spring 2009 Assignment Sheet
Date
Day
Lecture
Jan 5
M
Class Admin: Intro.Physics Phenomena
6
T
Problem solving and math
7
W
Units, Scalars, Vectors,
9
F*
Speed and Velocity
Jan 12
M
Acceleration
14
W
Free Falling Objects
16
F*
Projectile Motion
Jan 19
M
Martin Luther King
21
W
Newton’s Laws
23
F*
Mass and Weight
Jan 26
M
Motion with Friction
28
W
Review
29
Th
Test 1
30
F
Circular Motion
Feb 2
M
Planetary Motion and Gravity
4
W
Energy
6
F*
Harmonic Motion
Feb 9
M
Momentum
11
W
Impulse and Collisions
13Introduction
F*
Rotational
Section
0 Motion
Lecture 1 Slide 2
Feb 16
M
Presidents Day
17
Tu
Angular Momentum (Virtual Monday)
18
W
Review
19
H
Test 2
INTRODUCTION TO Modern Physics PHYX 2710
20
F*
Static Fluids, Pressure
Fall 2004
Feb 23
M
Flotation
25
W
Fluids in Motion
27
F*
Temperature and Heat
Mar 2
M
First Law of Thermodynamics
Physics of Technology—PHYS 1800
4
W Spring 2009Heat flow and Greenhouse
CircularEffect
Motion and
*Homework
Handout
6
F*
Climate Change
Chapter
Homework Due
1
App. B, C
1
2
2
3
3
1
No Class
4
4
2
4
1-4
1-4
5
3
5
6
6
4
7
7
8
5
No Class
8
5-8
5-8
9
9
9
10
6
10
10
Gravitational
Force
7
Lecture 12 Slide 2
Physics of Technology
PHYS 1800
Lecture 11
Circular Motion and
Gravitational Force
Introduction
Section 0
Lecture 1
Slide 3
Introduction and Review
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 3
Does the circular
motion of the moon
around the Earth ...
... have anything
inIntroduction
common
with
Section 0 Lecture 1
circular motion on
Earth?
Slide 4
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 4
Describing Motion and Interactions
Position—where you are in space (L or meter)
Velocity—how fast position is changing with time (LT-1 or m/s)
Acceleration—how fast velocity is changing with time (LT-2 or m/s2)
Force— what is required to change to motion of a body (MLT-2 or kgm/s2)
We will focus on a special kind of force, termed a central forces that
results from change in direction of velocity.
Introduction
Section 0
Lecture 1
Slide 5
Now look at a specific central force, the force due to gravity.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 5
Newton’s Laws in Review
•
1st Law —a special case of the 2nd Law for statics,
with a=0 or Fnet=0
• An objects velocity remains unchanged, unless
a force acts on the object.
•
2nd Law (and 1st Law)—How motion of a object is
effected by a force.
– The acceleration of an object is directly
proportional to the magnitude of the imposed
force and inversely proportional to the mass of
the object. The acceleration is the same
direction as that of the imposed force.
F  ma
units : 1 newton = 1 N = 1 kg  m s2
•
Introduction
Section 0
Lecture 1
Slide 6
3rd Law —Forces come from interactions with
other objects.
• 
For every action (force), there is an equal but
opposite reaction (force).
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 6
The Math Approach
• We are going to explore a
different kind of central force
that is no longer constant, but is
proportional to 1/r2.
ag
 k/r2
v f  v0  at or
a
v f  vo
t
1 2
 vo  vo   v f vo 
d 
t    t  v0t  at
2
 2   2 2
We will take a pragmatic approach
(hindsight
is 20-20!)
Introduction
Section 0 Lecture 1 Slide
7
We simply replace the force of the “string”
with the force of gravity
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Tstring  Fgravity  k
r2
Circular Motion and Gravitational Force
Lecture 12 Slide 7
Physics of Technology
PHYS 1800
Lecture 11
Circular Motion and
Gravitational Force
Introduction
Section 0
Lecture 1
Slide 8
Historical Perspectives
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 8
Historical Perspective on Gravity
Hart’s list of most influential people in the
history of the world:
Newton (2)*
Einstein (10)
Galileo Galilei (12)*
Aristotle (13)***
Copernicus (19) *
Kepler (75) *
Explore a trail of
science from the
early Greeks
through work today
at USU to improve
our understanding
and scientific
models for the
interaction of two
masses through
gravity.
Introduction
Section 0
*(even though they got the wrong answer on the test)
Lecture
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Simmon’s list of most influential scientists in
the history of the world
Newton (1) * (and 2 and 6 and 40)
Einstein (2)
1 Galileo
Slide 9 Galilei (7) *
Copernicus (9) *
Kepler (10) *
Tyco Brahe (22) *
Aristotle (an honorable mentioned) ***
Circular Motion and Gravitational Force
Lecture 12 Slide 9
Historical Perspective on Gravity
Aristotle
Circular orbits
Geocentric
This works pretty
well for the orbits
of the Sun, Moon
Introduction
Section 0
and stars,
but not
so well for
planets.
Lecture 1
Slide 10
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 10
Historical Perspective on Gravity
Ptolemy
Epicycle orbits
Geocentric
This works pretty well
for the orbits of the
Sun, Moon and stars,
Introduction
Section
and a little
better
for0 Lecture
planets.
1
Slide 11
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 11
Planetary Motion
• Retrograde motion
occurs in a planet’s orbit
when the planet appears
to move against the
background of stars
Introduction
Section 0
Lecture 1
Slide 12
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 12
Historical Perspective on Gravity
Copernicus and
Galelio
Circular or Epicycle
orbits
Heliocentric
This works pretty well
for the orbits of the
Sun, Moon and stars,
Introduction
and a better
forSection 0 Lecture
planets. Cleans up the
retrograde motion
(mostly)
1
Slide 13
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 13
Historical Perspective on Gravity
So who is right?
Team Geo: Aristotle/Ptolemy
Team Helio: Copernicus/Galileo
Tyco Barhe
Enter the “last great
naked-eye astronomer.
A phenomenal set of
data showed
slight
Introduction Section 0 Lecture
inconsistencies in our
descriptions of
astronomical orbits.
1
Slide 14
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 14
Historical Perspective on Gravity
Kepler
Tycho’s assistant
painstakingly analyzed all
that careful data.
This works pretty well
for the orbits of the
Sun, Moon
and stars,
Introduction Section 0 Lecture
and a little better for
planets.
1
Slide 15
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 15
Kepler’s First Law of Planetary Motion
Kepler was able to show that the orbits of the planets
around the sun are ellipses, with the sun at one focus.
Introduction
Section 0
Lecture 1
Slide 16
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 16
Kepler’s Second Law of Planetary Motion
• Because planets
move faster when
nearer to the sun, the
radius line for each
planet sweeps out equal
areas in equal times.
Introduction
Section 0
Lecture 1
Slide 17
• The two blue sections
each cover the same
span of time and have
equal area.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 17
Kepler’s Third Law of Planetary Motion
• The period (T) of an
orbit is the time it takes for
one complete cycle
around the sun.
• The cube of the average
radius (r) about the sun is
proportional to the square
of the period of the orbit.
Introduction
Section 0
Lecture 1
T r
2
3
Slide 18
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 18
Historical Perspective on Gravity
Newton
Enter Newton to tie it
all up in a neat
bundle
Found the form of the
force that fit into
Newton’s Laws that
fully explained all the
planetary
observations (except
very detailed
orbital
Introduction
Section 0
motion and
precessions).
Lecture 1
Slide 19
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 19
Historical Perspective on Gravity
Newton
To get
Kepler’s Laws of Planetary Motion
to match with
Newton’s Laws of (general) Motion
Fcentripetal  v
Newton set the centripetal force to a
central force proportional to 1/r2.
Introduction
Section 0
Lecture 1
2
r
k
r2
 Fgravity
Slide 20
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 20
Physics of Technology
PHYS 1800
Lecture 11
Circular Motion and
Gravitational Force
Introduction
Section 0
Lecture 1
Slide 21
Newton’s Universal Law of Gravitation
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 21
Newton’s Law of Universal Gravitation
•
Newton recognized the similarity
between the motion of a projectile on
Earth and the orbit of the moon.
•
If a projectile is fired with enough
velocity, it could fall towards Earth
but never reach the surface.
•
The projectile would be in orbit.
•
Newton’s law of universal gravitation
says the gravitational force between
two objects is proportional to the
mass of each object, and inversely
proportional to the square of the
distance between the two objects.
Introduction
•
Section 0
Lecture 1
Slide 22
G is the Universal gravitational
constant G.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Fgravity 
Circular Motion and Gravitational Force
Gm1m2
r2
Lecture 12 Slide 22
Historical Perspective on Gravity
Cavendish
Developed a clever way to measure
the weak gravitational force between
small masses.
Confirmed Newton’s Law of Universal
Gravitation (and in essence measured
the mass of the Earth in comparison
GmM earth
Fgravity 
to the kg mass standard).
r2
The effect the 320 kg balls of the 1.5 kg
balls was about
that of a grain of sand!
Introduction Section 0 Lecture 1 Slide 23
That’s 20 parts per billion precision!!!
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Wikeapedia has a nice description
of the experiment.
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 23
Historical Perspective on Gravity
Cavendish
Fgravity 
Measured the mass of the Earth in
comparison to the kg mass standard.
Introduction
Section 0
Lecture 1
so
g
Set weight equal to gravitational
attraction, then solved for (little) g.
GmM earth
 mg  W
2
rearth
GM earth
2
rearth
Slide 24
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 24
Physics of Technology
PHYS 1800
Lecture 11
Circular Motion and
Gravitational Force
Introduction
Section 0
Lecture 1
Slide 25
Extensions to Newton’s Law of Gravitation
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 25
Three equal masses are located as shown. What is the
direction of the total force acting on m2?
a)
b)
c)
d)
To the left.
To the right.
The forces cancel such that the total force is zero.
Section 0toLecture
1 Slide 26
It Introduction
is impossible
determine
from the figure.
There will be a net force acting on m2 toward m1. The third mass
exerts a force of attraction to the right, but since it is farther away
that force is less than the force exerted by m1 to the left.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 26
Extensions to Newton’s Theory of Gravity
Complex Motion Problems
Consider the Sun, Earth, Moon
system (the three body problem).
Fgravity 
GmM earth
r2
Approximating the complex forces
using Newton’s Laws leads to very
accurate solutions to the problem.
Introduction
Section 0
Lecture 1
Slide 27
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 27
The Moon and Other Satellites
Phases of the moon
result from the changes in
the positions of the moon,
Earth, and sun.
Introduction
Section 0
Lecture 1
Slide 28
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 28
An artist depicts a portion of the night sky as shown.
Is this view possible?
a) Yes
b) No
No. There are no stars
between the Earth and
the moon. (Maybe
Section 0
blinking Introduction
lights of a
passing jet?)
Lecture 1
Slide 29
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 29
Extensions to Newton’s Theory of Gravity
Complex Motion Problems
NASA predicts elaborate orbits for
spacecraft like the Solar Probe
Mission to the Sun or the CassiniHuygens Mission to Saturn and its
moons.
Introduction
Section 0
Lecture 1
Slide 30
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 30
Extensions to Newton’s Theory of Gravity
But…
Using retroreflectors left by
the Apollo astronauts, we
measure the moon's distance
with staggering precision:
better than a few cm out of
385,000 km (about 20 parts per
trillion!!!)
Results of this long-term experiment are:
• The moon is spiralling away from Earth at a
rate of 38 mm/yr.
• The moon probably has a liquid core of about
20% of the Moon's radius.
• The universal force of gravity is very stable.
The experiments have put an upper limit on the
change in G of less than 1 part in 1011 since
1969.
• Results strongly supporting the validity of
the Strong Equivalence Principle.
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Slide 31
• Einstein’s General Theory of Relativity
predicts the moon's orbit to within the
accuracy of the laser ranging measurements.
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 31
Extensions to Newton’s Theory of Gravity
Einstein’s Special Theory of Relativity
Based on how E&M works, Einstein postulated:
• The laws of physics are the same for all observers in uniform motion
relative to one another (Galileo’s principle of relativity),
• The speed of light in a vacuum, c, is the same for all observers,
regardless of their relative motion or of the motion of the source of the
light.
Some surprising results these are:
Relativity of simultaneity: Two events, simultaneous for some observer,
may not be simultaneous for another observer if the observers are in
relative motion.
Introduction
Section 0clocks
Lecture are
1 Slide
32
Time dilation:
Moving
measured
to tick more slowly than an
observer's "stationary" clock.
Length contraction: Objects are measured to be shortened in the direction
that they are moving with respect to the observer.
Mass-energy equivalence: E = mc2.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 32
Extensions to Newton’s Theory of Gravity
General Theory of Relativity
Einstein’s theory special relativity and Newton's law of universal
gravitation.
Equivalence Principle:
Inertial mass in Newton's second law, F = ma, mysteriously equals
the gravitational mass in Newton's law of universal gravitation
Classical tests predicted by Einstein
Introduction Sectionverified)
0 Lecture 1 Slide 33
(and subsequently
• Perihelion precession of Mercury
• Deflection of light by the Sun
• Gravitational redshift of light
Fgravity 
GmM earth
r2
R  12 g  R  g   
INTRODUCTION TO Modern Physics PHYX 2710
8 G
T
4
c
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 33
Extensions to Newton’s Theory of Gravity
Current Problems in Gravity
Is Einstein’s General Theory of Relativity the final word? (Maybe not)
Do gravitational waves exist? (Yes, maybe)
Are G and Λ truly constants? (Controversial evidence say NO!)
What happens when black holes (or galaxies) collide?
Can General Relativity be merged with Quantum Mechanics?
(QM has been tested to 17 decimal places- ~10 parts per quintillion,
Introduction
Lecture 1
Slide 34
even though
we Section
don’t0 really
understand
how to interpret the theory.)
Is there a 5th force in nature?
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 34
USU Perspective on Gravity
Hart’s list of most influential people in the
history of the world:
Newton (2)*
Einstein (10)
Galileo Galilei (12)*
Aristole (13)***
Copernicus (19) *
Kepler (75) *
Work today at USU
Larsen, Torre and Wheeler
*(even though they got the wrong answer on the test)
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Simmon’s list of most influential scientists in
the history of the world
Newton (1) * (and 2 and 6 and 40)
Einstein (2)
Slide 35 Galilei (7) *
Galileo
Copernicus (9) *
Kepler (10) *
Tyco Brahe (22) *
Aristole (an honorable mentioned) ***
Circular Motion and Gravitational Force
Lecture 12 Slide 35
Physics of Technology
PHYS 1800
Lecture 11
Circular Motion and
Gravitational Force
Introduction
Section 0
Lecture 1
Slide 36
Comments on the Nature of Scientific Theories
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 36
Lessons from the Theory of Gravity
Scientific Theories Are NOT Static
Aristotle was extended by Ptolemy,
who was corrected by Copernicus,
who was generalized by Galileo,
who was supplemented by Brahe,
who provided Kepler with data,
who was merged with laws of motion by Newton,
who was quantified by Cavendish,
who was supplanted by Einstein,
who was expanded by Einstein himself,
who was tested by 20th century scientists
Introduction
0 Lecture 1 by
Slide
37 and cosmology…
andSection
challenged
QM
But they can describe a lot of what goes on in the world around us.
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 37
Lessons from the Theory of Gravity
Scientific Theories are descriptions of nature, based
ultimately on our observations…
But they do not attempt to state what their origins are
or why they exist.
Scientific theories address where, when and how, but
not whyIntroduction Section 0 Lecture 1 Slide 38
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 38
Physics of Technology
Next Lab/Demo:
Circular Motion & Gravity
Energy & Oscillations
Thursday 1:30-2:45
ESLC 53
Ch 5
Next Class:
Wednesday 10:30-11:20
Slide 39
BUS
318 room
Read Ch 5
Introduction
Section 0
Lecture 1
INTRODUCTION TO Modern Physics PHYX 2710
Fall 2004
Physics of Technology—PHYS 1800
Spring 2009
Circular Motion and Gravitational Force
Lecture 12 Slide 39