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Chapter2_12

# Chapter2_12 - the earth 2 2 8 9 s m R M G g earth earth ≈...

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PHY3063 R. D. Field Department of Physics Chapter2_12.doc University of Florida Equivalence of Inertial and Gravitational Mass Inertial Mass: The inertial mass of an object tells us how difficult it is to change the particles velocity ( i.e. accelerate it). Can uniquely determine the inertial mass m of a particle relative to the reference mass m ref by applying an equal force to m and m ref and measuring the ratio of the resulting accelerations as follows: ref ref i a m F a m = = and ref ref i m a a m = . Gravitational Mass: The gravitational mass m g of a particle is determined ( at the surface of the earth ) by measuring the gravitational force exerted on it as follows: g m R M m G F g earth earth g grav = = 2 and g F m grav g = , where g is the acceleration due to gravity at the surface of
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Unformatted text preview: the earth: 2 2 / 8 . 9 s m R M G g earth earth ≈ = . Experiment: In a vacuum all bodies fall with the same acceleration. g m a m g m a m g i g i 2 2 2 1 1 1 ) ( ) ( ) ( ) ( = = Dividing the two equations gives = 1 2 2 2 1 1 ) ( ) ( ) ( ) ( a a m m m m g i g i and since a 1 = a 2 2 2 1 1 ) ( ) ( ) ( ) ( g i g i m m m m = . We see that m i /m g is the same for all particles and hence we can define G such that m i = m g for all particles. Only one type of mass! Earth M e R e Mass m g Cannon Ball Feather Release both at t = 0 Both hit ground at same time! Inertial Mass F m i Gravitational Mass Set equal to 1...
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