Transcript Gravitational Force

Physics 111 SI
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F= -G ( m1 * m2 / r^2 )
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g = G ( Me / Re^2) = G ( Me / ( Re +h)^2)
W = G ( Me * m / Re^2)
V = (G * Me / r ) ^1/2
T= 2пr ^ 3/2 / ( G * Me)^1/2
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G = 6.67*10^-11 N.m^2/kg^2
T is proportional to r^3/2
U = -G ( m * Me / r )
E= K + U = .5mv^2 + -G ( m * Me / r )
Conservation of Angular Momentum:
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Ii Wi = If Wf  For elliptical orbits: ra va = rp vp
6. Planets A, B and C are identical. A and C
have a giant moon orbiting them, while B has
a lightweight artificial satellite orbiting it, as
shown in the diagram. Which planet has the
strongest gravitational interaction with its
satellite?
a. Planet A, because its moon is heavy and close
to it.
b. Planet B, because only a lightweight object
can orbit without falling down.
c. Planet C, because it can interact with a heavy
object that is far away.
d. All have the same gravitational attraction,
because the planets are all the same mass.
e. Not enough information to determine.
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Why?
 Use equation
 F= -G ( m1 * m2 / r^2 )
 Plant A has the shortest r and
greatest m2 weight, producing
the greatest Force value
Why doesn’t the gravitational pull between
the Sun and the planets cause the planets
to fall into the Sun?
a. The background stars pull back on the
planets.
b. The Sun’s magnetic fields are pushing out.
c. The speed of the planets flings them out.
d. The Sun’s rotation pushes the planets out.
Satellites B is three times more massive than A, but
orbiting the planet at three times the distance.
a. A experiences a stronger force than B, because
differences in distance are more influential than
differences in mass.
b. B experiences a stronger force than A, because
differences in mass are more influential the
differences in distance.
c. A and B experience the same force, because
differences in distance are exactly compensated by
differences in mass.
d. A and B experience no force, because they are in
space.
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a. A experiences a stronger force
than B, because differences in
distance are more influential than
differences in mass.
Distance is squared, so it affects the
force at an exponential rate , as an
increase in mass progresses linearly
Planet A experiences
a gravitational force
by Planet C that is ______ that by Planet
B.
a. less than
b. equal to
c. greater than
d. cannot be
determined with the
given information.
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Equal to!
 A to B force:
 F= -G ( m1 * m2 / r^2 )
 F= -G ( 1 *1 / 1^ 2) = 1
A to C force:
F= -G ( m1 * m2 / r^2 )
F= -F ( 1 * 4 / 2^2) = 4/4 = 1
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Determine the force of gravitational attraction
between the earth (m = 5.98 x 1024kg) and a 70kg physics student if the student is in an
airplane at 40000 feet above earth's
surface. This would place the student a
distance of 6.39 x 106 m from earth's center.
F= -G ( m1 * m2 / r^2 )
 G = 6.67*10^-11 N.m^2/kg^2
 F = (6.67*10^-11)(5.98 x 1024)(70)
/ (6.39 * 10 ^6)
 F= 684 Newtons
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Suppose that you have a mass of 70 kg
(equivalent to a 154-pound person). How
much mass must another object have in
order for your body and the other object
to attract each other with a force of 1Newton when separated by 10 meters?
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m = 2.14 x 1010 kg
Use the equation Fgrav = G • m1 • m2 / d2
where m1 = 70 kg, d = 10 m and G = 6.673 x 1011N•m2/kg2.
Substitute and solve for m2.
Note that the object is equivalent to an
approximately 23 million ton object!! It takes a
large mass to have a significant gravitational
force.
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The average orbital distance of Mars
is 1.52 times the average orbital
distance of the Earth. Knowing that
the Earth orbits the sun in
approximately 365 days, use
Kepler's law of harmonies to predict
the time for Mars to orbit the sun.
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Given: Rmars = 1.52 • Rearth and Tearth = 365 days
Use Kepler's third law to relate the ratio of the
period squared to the ratio of radius cubed
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T is proportional to r^3/2
(Tmars)2 / (Tearth)2 • (Rmars)3 / (Rearth)3(Tmars)2 =
(Tearth)2 • (Rmars)3 / (Rearth)3
(Tmars)2 = (365 days)2 * (1.52)3
(Note the Rmars / Rearth ratio is 1.52)
Tmars = 684 days