Gravity
http://www.sritweets.com/wp-content/uploads/2010/08/gravitational-force.jpg
The thing that causes objects to fall
to Earth
http://www.physicsclassroom.com/Class/circles/u6l3a.cfm
http://www.physicsclassroom.com/Class/circles/u6l3b.cfm
http://www.physicsclassroom.com/Class/circles/u6l3c.cfm
Gravity and acceleration
• Force of gravity causes an
acceleration
• Acceleration due to gravity’s
force -- acceleration
experienced by object when
the only force acting on it is
force of gravity
• Approximately 9.8 m/s/s for
all objects on earth,
regardless of their mass
http://3.bp.blogspot.com/-q9_FtbtGGHA/TbSTRyr58I/AAAAAAAAABE/6INc8LHksSs/s1600/aviao-e-paraquedista-a858e.jpg
Kepler and planetary motion
• Early 1600's Johannes Kepler
develop three laws to describe
the motion of planets about the
sun
• 1. Paths of planets are elliptical
with center of sun at one focus
• 2. Imaginary line drawn from
center of sun to center of planet
will sweep out equal areas in
equal intervals of time (periods)
• 3. Ratio of squares of periods
(times) of any two planets equals
ratio of the cubes of their
average distances from sun
http://library.thinkquest.org/03oct/02144/pics/basics/kepler2.png
http://rst.gsfc.nasa.gov/Sect19/Kepler3a.JPG
Newton wondered . . .
• What causes elliptical motion
of planets?
• What causes circular motion
of moon about earth?
• Requires an unbalanced force
• Suppose cannonball could be
fired such that trajectory of
falling cannonball matched
curvature of earth. If such a
speed was obtained, then
cannonball would fall around
earth instead of into it. Orbit!
http://hildaandtrojanasteroids.net/TA32Newtonthought.jpg
Newton’s thoughts (cont.)
• At even greater launch
speeds, cannonball would
orbit the earth, but in
elliptical path
• Orbiting moon can be
compared to falling
cannonball, or even falling
apple
• Same force that causes
objects on Earth to fall to
earth also causes objects
in heavens to move along
circular and elliptical paths
http://tap.iop.org/fields/gravity/401/img_full_46817.gif
Apple and Moon
• Apple accelerates
towards earth at rate of
9.8 m/s2
• Moon accelerates
towards earth at rate of
0.00272 m/s2
• So more distant moon
accelerates at rate
approximately 1/3600
the acceleration of the
apple
http://www.8planets.co.uk/wpcontent/themes/8planets/images/red_apple_lg.jpg
http://library.thinkquest.org/C007571/images/moon.jpg
Distance tells part of story
• Compare distance from apple to
center of earth with distance from
moon to center of earth
• Moon in orbit about earth is
approximately 60 times further
from earth's center than apple
• Moon experiences force of gravity
1/(60)2 times that of apple
• Force of gravity follows an inverse
square law. (Squaring distance
greatly reduces gravitational force)
http://www.physics.uc.edu/~hanson/ASTRO/LECTURENOTES
/F04/GRAVITYLIGHT/Page1_files/InvSqLaw.gif
Gravity and distance
• Relationship between
amount of gravitational
force and distance.
• (Fgrav) between earth and
any other object and
distance that separates
their centers (d) can be
expressed as:
http://www.math.ubc.ca/~cass/courses/m308/projects/lim
/images/UniversalLawOfGravitation1.GIF
Check Understanding
• 1 . Suppose two objects attract each other with
gravitational force of 9 units. If distance between
two objects is doubled, what is the new force of
attraction between the two objects?
• If the distance is increased by a factor of 2, then
force will be decreased by a factor of 4 (22). The
new force is then 1/4 of the original 9 units.
• F = (9 N) / 4 = 2.25 units
Check Understanding
• 2. Suppose that two objects attract each other
with a gravitational force of 16 units. If the
distance between the two objects is tripled, then
what is the new force of attraction between the
two objects?
• If the distance is increased by a factor of 3, then
force will be decreased by a factor of 9 (32). The
new force is then 1/9 of the original 16 units.
• F = (16 N) / 9 = 1.78 units
Check Understanding
• 3. Noah Formula has devised a new business plan
based on his teacher's Physics for Better Living
theme. Noah learned that objects weigh different
amounts at different distances from Earth's
center. His plan involves buying gold by the
weight at one altitude and then selling it at
another altitude at the same price per weight.
Should Noah buy at a high altitude and sell at a
low altitude or vice versa?
• To profit, buy at a high altitude and sell at a low
one
Newton’s laws of motion and gravity
• Newton concluded that gravity
depends upon distance
• Newton also knew force that
causes a falling stone’s
acceleration (gravity) must be
dependent upon mass of the
stone
• But since the force acting to
cause a stone's downward
acceleration also causes earth's
upward acceleration (Newton's
third law), gravitational force
must also depend upon mass of
earth
http://images.tutorvista.com/content/gravitation/newtons-thiirdlaw-of-motion.jpeg
Law of Universal Gravitation
• Force of gravity acting between
earth and any other object is
directly proportional to the mass
of the earth, directly proportional
to the mass of the other object,
and inversely proportional to the
square of the distance that
separates the centers of the earth
and the object
• ALL objects attract each other
with gravitational force
• (Note: gravitational forces are
always attractive, pulling objects
toward each other)
http://www.math.ubc.ca/~cass/courses/m308/projects/lim/images/Unive
rsalLawOfGravitation1.GIF
Mass and gravity
• As mass of either object increases, the force of
gravitational attraction between them also increases
• If mass of 1 of objects is doubled, then force of
gravity between them is doubled. If the mass of 1 of
objects is tripled, then force of gravity between them
is tripled
http://www.tech-faq.com/wp-content/uploads/images/Universal-Gravitation.gif
Combining mass and distance
• Effects of mass and distance
Law of universal gravitation
• Determine the force of gravitational attraction
between the earth (m = 5.98 x 1024 kg) and a 70-kg
physics student if the student is in an airplane at
40,000 feet above earth's surface. This would place the
student a distance of 6.39 x 106 m from earth's center.
Variable force of gravity
• What you
weigh depends
on where you
are!
Gravitational attraction
• Gravitational interactions
exist between all objects
with an intensity that is
directly proportional to
the product of their
masses
• So as you sit in your
classroom, you are
gravitationally attracted
to the people around you,
to the table you are
working at, and to
equipment near you
http://www.physics.uwa.edu.au/__data/assets/image/0006/1181346/2006
_69_Janelle.jpg
Check understanding
• Suppose two objects attract each other with a
gravitational force of 16 units. If distance
between the objects is reduced in half, what is
the new force of attraction between the two
objects?
• If the distance is decreased by a factor of 2, then
force will be increased by a factor of 4 (22). The
new force is then 4 times the original 16 units.
• F = (16 units) • 4 = 64 units
Check understanding
• Suppose two objects attract each other with a
gravitational force of 16 units. If the mass of both
objects was doubled, and the distance between
the objects remained the same, what would be
the new force of attraction between them?
• If each mass is increased by a factor of 2, then
force will be increased by a factor of 4 (2*2). The
new force is then 4 times the original 16 units.
• F = (16 units ) • 4 = 64 units
Check understanding
• Suppose two objects attract each other with a
gravitational force of 16 units. If the mass of object 1
was doubled, and if the distance between the objects
was tripled, then what would be the new force of
attraction between the two objects?
• If the mass of one object is doubled, the force of
attraction will be doubled as well. But this affect is
more than offset by the tripling of the separation
distance. Tripling the distance would cause the force to
be decreased by a factor of 9 (32). The net affect on
force is that it decreased by a factor of 2/9.
• F = (16 units) • 2 / 9 = 3.56 units
Check understanding
• Anita Diet is very concerned about her weight
but seldom does anything about it. After
learning about Newton's law of universal
gravitation in Physics class, she becomes all
concerned about the possible affect of a
change in Earth's mass upon her weight.
During a (rare) free moment at the lunch
table, she speaks up "How would my weight
change if the mass of the Earth increased by
10%?" How would you answer Anita?
Check understanding
• Answer: "Anita - that's a great question! Since
your weight is directly dependent upon the
mass of the Earth, you would weigh 10%
more. But don't worry, honey. You wouldn't
look any different than you do now since your
mass would remain as is."
Results of gravitation
• Tides
http://ircamera.as.arizona.edu/NatSci102/NatSci102/images/neaptide.jpg
• Force fields
http://www.rodstrom-nopo.com/wp-content/gallery/nopo-science/gravity1.jpg
Results of gravitation
• Orbital motion
http://cnx.org/content/m20337/latest/graphics8.png
• Black holes
http://news.bbc.co.uk/olmedia/520000/images/_523161_black_hole300.jpg