Q08.Gravity

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Q08. Gravity
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• Which is the most efficient way to launch a
  satellite?
• ???????????????
• Westward at low latitudes. ???????
• Eastward at low latitudes. ???????
• Westward at high latitudes. ???????
• Eastward at high latitudes. ???????

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• Earth turns from west to east.
• A stationary object on earth has a tangential
  velocity vT pointing to the east.
• vT is largest at the equator.

E
W
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• Consider a planet in an elliptical orbit around
  the sun.
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• Let WT be the work done by the gravitational
  force of the sun on the planet over a short
  period of time T, and W be the work done over a
  complete orbit of the planet.
• ? WT ??????????????? T ?????,W ????????????????
• Which of the following statement is true?
• ???????????
• WT ?? 0 , W ? 0.
• WT ?? 0 , W ¹ 0
• WT ?¹ 0 , W ? 0
• WT ?¹ 0 , W ¹ 0

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Elliptical orbit ? F ? dr ? 0 ? WT ?
0 Gravity is conservative ? W 0
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• Which point in the orbit has the lowest orbital
  velocity?
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• A
• B
• C
• D

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? v is smallest when r is largest.
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• Suppose the paths in the figure are the paths of
  four projectiles.
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• All four projectiles were launched from a common
  point at the top of the figure. ????????????????
• Which projectile had the second-highest initial
  speed?
• ??????????????
• The projectile with the closed circular path.
• ??????????
• The projectile with the hyperbolic path.
• ???????????
• The projectile with the parabolic path.
• ???????????
• The projectile with the elliptical path.
• ???????????

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E K ordering from smallest to largest.
3
2
1
1
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• Suppose Spacecraft A and Spacecraft B are in
  circular orbits around the Earth, with Spacecraft
  B at a higher altitude.
• ????? A ? B ???????????,? B ????
• Which one of the following statements is true?
• ????????????
• Spacecraft B has greater kinetic energy K.
• ??? B ?????? K?
• A larger proportion of spacecraft B's total
  energy is kinetic. ??? B ?????,?????????
• Spacecraft B has greater total energy, E.
• ??? B ??????? E?
• None of the above statements are true.
• ?????

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• Spacecraft B has greater kinetic energy K.
• ??? B ?????? K?
• A larger proportion of spacecraft B's total
  energy is kinetic. ??? B ?????,?????????
• Spacecraft B has greater total energy, E.
• ??? B ??????? E?
• None of the above statements are true.
• ?????

?
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• If the mass of the Earth were suddenly increased
  four times, its new period around the Sun
  compared to the original period would be
• ?????????????,??????????????????
• four times greater. ?????
• two times greater. ?????
• four times smaller. ?????
• two times smaller. ?????
• unchanged. ???

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?
New orbit
?
?
?
?
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• Which of the following is true about artificial
  satellites in Earth's orbit?
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• The speed required to keep a satellite in a given
  orbit is proportional to the mass of the
  satellite.
• ???????????????????????
• The satellite's period of revolution about the
  Earth is independent of its orbital radius.
• ??????????????????
• The speed of a satellite in a circular orbit can
  vary.
• ?????????,????????
• All the orbits for artificial satellites are
  circular.
• ????????????
• A satellite in a larger circular orbit always has
  a longer orbital period than a satellite in a
  smaller circular orbit.
• ???????????,??????????????????

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• The speed required to keep a satellite in a given
  orbit is proportional to the mass of the
  satellite.
• ???????????????????????
• The satellite's period of revolution about the
  Earth is independent of its orbital radius.
• ??????????????????
• The speed of a satellite in a circular orbit can
  vary.
• ?????????,????????
• All the orbits for artificial satellites are
  circular.
• ????????????
• A satellite in a larger circular orbit always has
  a longer orbital period than a satellite in a
  smaller circular orbit.
• ???????????,?????????????????

is indep of m.
Elliptical in general.
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• Each of the four corners of a square with edge a
  is occupied by a point mass m. There is a fifth
  mass, also m, at the center of the square. To
  remove the mass from the center to a point far
  away the work that must be done by an external
  agent is given by
• 4Gm2/a
• 4Gm2/a
• (4?2) Gm2/a
• (4?2) Gm2/a
• 4Gm2/a2

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Potential energy of m at center of square is
To bring it to infinity, where
requires work
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• A projectile is fired straight upward from
  Earth's surface with a speed that is half the
  escape speed. If R is the radius of Earth,
  the highest altitude reached, measured from the
  surface, is
• R/4
• R/3
• R/2
• R
• 2R

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By definition
Maximum height H is given by
( Energy conservation )
?
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• An object is dropped from an altitude of one
  Earth radius above Earth's surface. If M is the
  mass of Earth and R is its radius the speed of
  the object just before it hits Earth is given by
  

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Energy conservation