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posted by  Bakey on 7/22/2009 8:10:17 PM  |  status: Live  |  Earned Karma: 43

Universal Gravitational Constant

Course Textbook Chapter Problem Needs by
General Physics Physics for Scientists and Engineers 7th by Serway, Jewett 13 N/A N/A
Question Details:
An object is released from rest at a distance h above the surface of a planet (mass = M, radius = R). With what speed will the object strike the surface of the planet? Disregard any dissipative effects of the atmosphere of the planet.
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posted by VSL on 7/22/2009 8:21:06 PM  |  status: Live
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Response Details:
Note: apply conservation of energy
Note: gravitational potential energy is mathematically defined as

Solution:
"In physics, you don't have to go around making trouble for yourself - nature does it for you" - Frank Wilczek
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posted by MasterChef on 7/22/2009 8:29:31 PM  |  status: Live
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Response Details:
We can use simple conservation of energy here:
Initially the energy is all potential:


The final energy is:




         M=mass of object           M'=mass of planet



If you do this problem any other way, like finding the acceleration caused by the force of gravity, you must realize, that the force of gravity is NOT constant. It depends on the distance between the two objects.  So you CANNOT use the simply kinetic equations since they deal with CONSTANT acceleration!
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