1710--Warm-up Physics Quiz
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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? A. B. C. D. About 5 m About 7 cm About 2 cm None of the above Answer Now !
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Physics 1710--Chapter 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 = g t 2 = 0.5 (0.14 m/s2)(1 sec)2 = 0.0 7 m = 7 cm
Physics 1710--Chapter 13 Apps: Gravity 1 Lecture
The gravitational force constant g is equal to g = G M/(R+h) 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 = [ 2GM/R]
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Physics 1710--Chapter 13 Apps: Gravity
Does the position of the moon affects us as astrology claims?
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Think!
No Talking! Confer! Peer Instruction Time
Physics 1710--Chapter 13 Apps: Gravity
Does the position of the moon affects us as astrology claims?
Answer Now ! A. B. C. D. Yes, I strongly agree Yes, I Agree No, I disagree No, I strongly disagree
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Physics 1710--Chapter 13 Apps: Gravity
Astrology: Does the moon affect us?
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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 g
d moon=3.84x108 m
M =7.36x1023 kg
Physics 1710--Chapter 13 Apps: Gravity Gravitational Potential Energy
U = -R Fd r U = -R G Mm/r 2d r U = GMm/R = mgR U = 0 as r F dr
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Physics 1710--Chapter 13 Apps: Gravity
Escape Velocity
If K is such that E = 0 as r , then KR = m v 2 = UR = GMm/ R and vescape = [ 2GM/R] = [2gR]
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UR = GMm/R K = m v2
U = 0 K = 0
Physics 1710--Chapter 13 Apps: Gravity
Were the astronauts in danger of jumping the off "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) Answer Now ! A. B. C. D. Yes. Definitely. Maybe. No. Definitely not. Not enough information.
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Physics 1710--Chapter 13 Apps: Gravity
Escape Velocity
vescape = [ 2GM/R] = [2gR] = [2(0.14 N/kg)(625 km)] ~ 400 m/s ~ 900 mph. Safe!
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vescape = [ 2GM/R] = [2gR]??
Physics 1710--Chapter 13 Apps: Gravity
Escape Velocity of Earth?
vescape = [ 2GM/R] = [2gR] = [2(9.8 N/kg)(6.3 x10 6 m)] ~ 11,000 m/s 25,000 mph. Stuck!
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vescape = [ 2GM/R] = [2gR]??
Physics 1710--Chapter 13 Apps: Gravity
Total Energy for Gravitationally Bound Mass E=K+U E = m v 2 GMm/r E = L2/2mr 2 GMm/r Bound orbit if E 0 and - dE/dr |r = 2 (L2/2mro) - GMm = 0
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E = - GMm/2ro
Physics 1710--Chapter 13 Apps: Gravity
Total Energy for Gravitationally Bound Mass E=K+U E = - GMm/2ro r
E<0
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L2 /2mr 2 GMm/r
ro = - 2E/(GMm)
Physics 1710--Chapter 13 Apps: Gravity
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 consta...