Phys 0174 Fall 2008 - Chapter 13, 4 slides

Phys 0174 Fall 2008 - Chapter 13, 4 slides - Chapter 13...

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1 Chapter 13 Gravitation ¾ Newton’s law of gravitation ¾ The acceleration of gravity on the surface of the earth, above it and below it. ¾ Gravitational potential energy ¾ Kepler’s three laws of planetary motion ¾ Satellites (orbits, energy, escape velocity) 2 m 1 m 2 The tendency of objects with mass to move towards each other Newton's Law of is known as gr Gravit avitati ation on. 12 has the following characteristics: 1. The force acts along the line that connects the two particles. 2. Its magnitude is given b Newton's la y the equat w of gra ion: vitation mm FG r = 2 11 2 2 Here and are the masses of the two particles, is the separation between them and is the gravitati . 6.67 onal 10 constant. N.m / g r k G G 2 ˆ G r = Fr G 3 m 1 m 2 F 12 F 21 r 12 1 2 21 2 1 The two forces in a gravitational pair obey Newton's third law. The gravitational force exerted on by is equal in magnitude and opposite in direction to the force exerted on by . F F G G G 12 21 0 += FF G 2 ˆ G r = G 4 The net gravitational force exerted by a group of particles is equal to the vecto Gravita r sum o tion and the Principle of S f the contribution from eac uperpos h parti ition cle. 11 2 3 12 13 1 2 1 3 23 1 For example the net force exerted on by and is equal to: Here and are the forces exerted on by and , respectively. In general the force exerted on mm m m m = + F F G GG G 21 31 4 1 1 2 by n particles is given by the equation: ... n ni i = =+++ FF F F F F GG G G G G 2 n i i = =
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5 m 1 dm r d F G 1 The gravitation force exerted by a continuous extended object on a particle of mass can be calculated using the principle of superposition. The object is divided into elements of mass and the n m dm 1 1 1 1 2 et force on is the vector sum of the forces exerted by each element. The sum takes the form of an integral: Here is the force exerted on by m dm d m Gm d dF dm r  =  =  F FF G G G 1 d = GG 6 12 1 2 Newton proved that a uniform shell attarcts a particle that is outside the shell as if the mass of the shell were concetrated at the center of the shell: mm FG r = m 1 m 2 r F 1 m 2 m 1 If the particle is inside the shell, the net force is z N e ote: ro.
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Phys 0174 Fall 2008 - Chapter 13, 4 slides - Chapter 13...

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