In the movie

1
In the movie Armaggedon a comet the size of
Texas (800 miles or 1250 km in diameter) was
heading for Earth. If the density were 800
kg/m3, the mass would be about 8.x10 20 kg. How
far would a ball on the surface fall in 1.0
second?
Physics 1710Warm-up Quiz

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1. About 5 m
2. About 7 cm
3. About 2 cm
4. None of the above

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Physics 1710Chapter 12 Apps Gravity
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• Gravitation

g G M/ R2 g(6.67x10-11 N m2/kg2)(8x1020
kg)/(625x103 m)2 g 0.14 N/kg d ½ g t 2 0.5
(0.14 m/s2)(1 sec)2 0.0 7 m 7 cm
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Physics 1710Chapter 13 Apps Gravity
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• 1' Lecture
• The gravitational force constant g is equal to
  g G M/(Rh) 2, M and R are the mass and
  radius of the planet.
• The gravitation field is the force divided by the
  mass.
• The gravitation potential energy for a point mass
  is proportional to the product of the masses and
  inversely proportional to the distance between
  their centers.
• The escape velocity is the initial velocity at
  the surface required to leave a body. vescape
  v 2GM/R

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Physics 1710Chapter 13 Apps Gravity
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• Does the position of the moon affects us as
  astrology claims?

Peer Instruction Time
5
Does the position of the moon affects us as
astrology claims?
Physics 1710Chapter 13 Apps Gravity

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1. Yes, I strongly agree
2. Yes, I Agree
3. No, I disagree
4. No, I strongly disagree

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Physics 1710Chapter 13 Apps Gravity
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• Astrology Does the moon affect us?
• F - G M m/ d 2

M 7.36x1023 kg d 3.84x108 m F/m
(7x10-11)(7x1023)/(4x108)2 3x10-4 N/kg 30 µ
g
d moon3.84x108 m
M 7.36x1023 kg
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Physics 1710Chapter 13 Apps Gravity
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• Gravitational Potential Energy
• U -?8R Fd r
• U -?8R G Mm/r 2d r
• U GMm/R mgR
• U 0 as r ?8

F
d r
8
Physics 1710Chapter 13 Apps Gravity
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• Escape Velocity
• If K is such that E 0 as r ?8, then
• KR ½ m v 2 UR GMm/ R
• and
• vescape v 2GM/R v2gR

U8 0
UR GMm/R
K8 0
K ½ m v 2
9
Were the astronauts in danger of jumping off the
Armaggedon comet? (Hint What is the escape
velocity from our Armaggedon comet? M 8x1020
kg, R 6.25x10 5 m, g 0.14 N/kg)
Physics 1710Chapter 13 Apps Gravity

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1. Yes. Definitely.
2. Maybe.
3. No. Definitely not.
4. Not enough information.

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Physics 1710Chapter 13 Apps Gravity
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• Escape Velocity
• vescape v 2GM/R v2gR
• v2(0.14 N/kg)(625 km) 400 m/s
• 900 mph. Safe!

vescape v 2GM/R v2gR??
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Physics 1710Chapter 13 Apps Gravity
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• Escape Velocity of Earth?
• vescape v 2GM/R v2gR
• v2(9.8 N/kg)(6.3 x10 6 m) 11,000 m/s
• 25,000 mph. Stuck!

vescape v 2GM/R v2gR??
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Physics 1710Chapter 13 Apps Gravity
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• Total Energy
• for Gravitationally Bound Mass
• E K U
• E ½ m v 2 GMm/r
• E L2/2mr 2 GMm/r
• Bound orbit if E 0 and
• - dE/dr ro 2 (L2/2mro) - GMm 0
• E - GMm/2ro

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Physics 1710Chapter 13 Apps Gravity
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• Total Energy
• for Gravitationally Bound Mass
• E K UE - GMm/2ro

r
L2 /2mr 2 GMm/r
E lt 0
ro - 2E/(GMm)
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Physics 1710Chapter 13 Apps Gravity
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• Summary
• The force of attraction between two bodies with
  mass M and m respectively is proportional to the
  product of their masses and inversely
  proportional to the distance between their
  centers squared.
• F - G M m/ r 2
• The proportionality constant in the Universal
  Law of Gravitation G is equal to 6.673 x 10 11 N
  m2 /kg2 .

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Physics 1710Chapter 13 Apps Gravity
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• Summary
• The gravitational force constant g is equal to
• G M/(Rh) 2, R is the radius of the planet.
• Keplers Laws
• The orbits of the planets are ellipses.
• The areal velocity of a planet is constant.
• The cube of the radius of a planets orbit
• is proportional to the square of the period.
• The gravitation field is the force divided by
  the mass.
• g Fg / m

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Physics 1710Chapter 13 Apps Gravity
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• Summary
• The gravitation potential energy for a point
  mass is proportional to the product of the masses
  and inversely proportional to the distance
  between their centers
• U GMm / r
• The escape velocity is the minimum speed a
  projectile must have at the surface of a planet
  to escape the gravitational field.
• vescape v 2GM/R
• Total Energy E is conserved for two body
  geavitational problem bodies are bound for E 0
• E L2/2mr 2 GMm/r