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Unformatted text preview: 1 General Relativity Hawley & Holcomb, Chapter 8 2 Equivalence Principle Lets imagine that you are in an elevator. What happens when the elevator begins to go up? What happens when the elevator begins to go down? What happens when the elevator moves at constant speed? What would happen when the wire on which the elevator is suspended is cut? Lets imagine that you are an astronaut on board a space station. Why do you think you are a weightless? What would you do to make gravity in flight? 3 Acceleration = Gravity Newtons 2 nd law of motion relates force to acceleration F = m a Newtons force of gravity relates gravitational force to the spatial distribution of other bodies F = m g Therefore, a = g , for a freely falling body But why were we justified in using the same mass? Mass can be measured in two completely different ways: Mass could be measured by applying a force and measuring acceleration Mass could be measured by measuring the gravitational force (weight) of an object In principle, these two masses may not have been the same. 4 Inertial Mass = Gravitational Mass Inertial mass, m inertial , may be defined by Inertial force = m inertial a Gravitational mass, m gravity , may be defined by Gravitational force = m gravity g Then, Newtons equation becomes m inertial a = m gravity g Simultaneously drop two objects with different masses from some height in the absence of air drag (inside vacuum tube on the Earth, or anywhere on the Moon), and they will reach the bottom simultaneously. Therefore, m inertial = m gravity 5 Equivalence Principle Gravity can be canceled or mimicked by acceleration: A small object in free fall does not experience gravity (the reason that only small objects in free fall are oblivious to gravity is explained on a following page). An object accelerating at a constant rate experiences the same conditions as a stationary object in a gravitational field. When gravity is canceled by acceleration, all the laws of physics, including the laws of special relativity, are still perfectly valid; the freefalling frame and the inertial frame are completely equivalent. Terminology: Freely falling frame is a reference frame, that is, the point of view of an observer, that experiences no force other than the force of gravity (examples: planets in the solar system, satellites and the international space station, space shuttle with its engines powered off are all in the state of free fall)....
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This note was uploaded on 09/14/2009 for the course AST 309 taught by Professor Johnlacy during the Spring '08 term at University of Texas at Austin.
 Spring '08
 JohnLacy

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