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Physics of Technology PHYS 1800

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Title: Physics of Technology PHYS 1800


1
Physics of Technology PHYS 1800
  • Lecture 12
  • Circular Motion and Gravitational Force

2
PHYSICS OF TECHNOLOGY Spring 2009 Assignment
Sheet
Homework Handout
3
Physics of Technology PHYS 1800
  • Lecture 11
  • Circular Motion and Gravitational Force

Introduction and Review
4
Does the circular motion of the moon around the
Earth ...
... have anything in common with circular motion
on Earth?
5
Describing Motion and Interactions
  • Positionwhere you are in space (L or meter)
  • Velocityhow fast position is changing with time
    (LT-1 or m/s)
  • Accelerationhow 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 kg-m/s2)
  • We will focus on a special kind of force, termed
    a central forces that results from change in
    direction of velocity.
  • Now look at a specific central force, the force
    due to gravity.

6
Newtons Laws in Review
  • 1st Law a special case of the 2nd Law for
    statics, with a0 or Fnet0
  • 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.
  • 3rd Law Forces come from interactions with other
    objects.
  • For every action (force), there is an equal but
    opposite reaction (force).

7
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.

? k/r2
We will take a pragmatic approach (hindsight is
20-20!) We simply replace the force of the
string with the force of gravity
8
Physics of Technology PHYS 1800
  • Lecture 11
  • Circular Motion and Gravitational Force

Historical Perspectives
9
Historical Perspective on Gravity
Harts list of most influential people in the
history of the world Newton (2) Einstein
(10) Galileo Galilei (12) Aristotle
(13) Copernicus (19) Kepler (75) (even
though they got the wrong answer on the test)
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.
Simmons list of most influential scientists in
the history of the world Newton (1) (and 2
and 6 and 40) Einstein (2) Galileo Galilei (7)
Copernicus (9) Kepler (10) Tyco Brahe (22)
Aristotle (an honorable mentioned)
10
Historical Perspective on Gravity
Aristotle Circular orbits Geocentric This
works pretty well for the orbits of the Sun, Moon
and stars, but not so well for planets.
11
Historical Perspective on Gravity
Ptolemy Epicycle orbits Geocentric This works
pretty well for the orbits of the Sun, Moon and
stars, and a little better for planets.
12
Planetary Motion
  • Retrograde motion occurs in a planets orbit when
    the planet appears to move against the background
    of stars

13
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, and a
better for planets. Cleans up the retrograde
motion (mostly)
14
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 inconsistencies in our descriptions of
astronomical orbits.
15
Historical Perspective on Gravity
Kepler Tychos assistant painstakingly analyzed
all that careful data. This works pretty well
for the orbits of the Sun, Moon and stars, and a
little better for planets.
16
Keplers 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.
17
Keplers 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.
  • The two blue sections each cover the same span
    of time and have equal area.

18
Keplers 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.

19
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
Newtons Laws that fully explained all the
planetary observations (except very detailed
orbital motion and precessions).
20
Historical Perspective on Gravity
Newton To get Keplers Laws of Planetary
Motion to match with Newtons Laws of (general)
Motion Newton set the centripetal force to a
central force proportional to 1/r2.
21
Physics of Technology PHYS 1800
  • Lecture 11
  • Circular Motion and Gravitational Force

Newtons Universal Law of Gravitation
22
Newtons 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.
  • Newtons 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.
  • G is the Universal gravitational constant G.

23
Historical Perspective on Gravity
Cavendish Developed a clever way to measure the
weak gravitational force between small
masses. Confirmed Newtons Law of Universal
Gravitation (and in essence measured the mass of
the Earth in comparison to the kg mass
standard). The effect the 320 kg balls of the
1.5 kg balls was about that of a grain of sand!
Thats 20 parts per billion precision!!! Wikeap
edia has a nice description of the experiment.
24
Historical Perspective on Gravity
Cavendish Measured the mass of the Earth in
comparison to the kg mass standard. Set weight
equal to gravitational attraction, then solved
for (little) g.
25
Physics of Technology PHYS 1800
  • Lecture 11
  • Circular Motion and Gravitational Force

Extensions to Newtons Law of Gravitation
26
Three equal masses are located as shown. What is
the direction of the total force acting on m2?
  1. To the left.
  2. To the right.
  3. The forces cancel such that the total force is
    zero.
  4. It is impossible to 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.
27
Extensions to Newtons Theory of Gravity
Complex Motion Problems Consider the Sun,
Earth, Moon system (the three body
problem). Approximating the complex forces using
Newtons Laws leads to very accurate solutions to
the problem.
28
The Moon and Other Satellites
  • Phases of the moon result from the changes in
    the positions of the moon, Earth, and sun.

29
An artist depicts a portion of the night sky as
shown. Is this view possible?
  • Yes
  • No

No. There are no stars between the Earth and the
moon. (Maybe blinking lights of a passing jet?)
30
Extensions to Newtons Theory of Gravity
Complex Motion Problems NASA predicts elaborate
orbits for spacecraft like the Solar Probe
Mission to the Sun or the Cassini-Huygens
Mission to Saturn and its moons.
31
Extensions to Newtons 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.
  • Einsteins General Theory of Relativity
    predicts the moon's orbit to within the accuracy
    of the laser ranging measurements.

32
Extensions to Newtons Theory of Gravity
  • Einsteins Special Theory of Relativity
  • Based on how EM works, Einstein postulated
  • The laws of physics are the same for all
    observers in uniform motion relative to one
    another (Galileos 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.
  • Time dilation Moving clocks are 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.

33
Extensions to Newtons Theory of Gravity
  • General Theory of Relativity
  • Einsteins 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
  • (and subsequently verified)
  • Perihelion precession of Mercury
  • Deflection of light by the Sun
  • Gravitational redshift of light

34
Extensions to Newtons Theory of Gravity
Current Problems in Gravity Is Einsteins
General Theory of Relativity the final word?
(Maybe not) Do gravitational waves exist? (Yes,
maybe) Are G and ? 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, even though we
dont really understand how to interpret the
theory.) Is there a 5th force in nature?
35
USU Perspective on Gravity
Work today at USU Larsen, Torre and Wheeler
Harts list of most influential people in the
history of the world Newton (2) Einstein
(10) Galileo Galilei (12) Aristole
(13) Copernicus (19) Kepler (75) (even
though they got the wrong answer on the test)
Simmons list of most influential scientists in
the history of the world Newton (1) (and 2
and 6 and 40) Einstein (2) Galileo Galilei (7)
Copernicus (9) Kepler (10) Tyco Brahe (22)
Aristole (an honorable mentioned)
36
Physics of Technology PHYS 1800
  • Lecture 11
  • Circular Motion and Gravitational Force

Comments on the Nature of Scientific Theories
37
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
and challenged by QM and
cosmology But they can describe a lot of what
goes on in the world around us.
38
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 why
39
Physics of Technology
  • Next Lab/Demo Circular Motion Gravity
  • Energy Oscillations
  • Thursday 130-245
  • ESLC 53
  • Ch 5
  • Next Class Wednesday 1030-1120
  • BUS 318 room
  • Read Ch 5
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