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Phy 121
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Still Not Clear on my Question
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We obtain velocities
vel. at radius 7.6 = `sqrt ( 6.906 m/s^2 * 7.6 * 10 ^ 6 meters) = 7.244 * 10^3 m/s, and
vel. at radius 7.75 = `sqrt ( 6.641 m/s^2 * 7.75 * 10 ^ 6 meters) = 7.174 * 10^3 m/s
For the `mass kg mass of the satellite we easily obtain kinetic energies of 110100 MJ (megaJoules) and 108000 MJ. The kinetic energy difference is therefore
KE change = ( 108000 - 110100) MJ = -2100 MJ
The midpoint orbital radius is 7.675, which implies a midpoint gravitational field of
midpoint field = ( 7.675 / rEarth) ^ -2 * 9.8 m/s^2 = 6.771 m/s^2,
and gravitational force of
midpoint gravitational force = `mass kg * 6.771 m/s^2 = 28430 N.
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I still am not understanding how there is not a mass that goes into m for the KE and the midpoint gravitational force. I have scoured the internet and for any reference of these types of problems there is a given mass and I cannot find anything about a mass `kg mass. Even above of the midpoint. If you divide the 28430 N / 6.771 m/s^2 = 4,198.7890 kg. Then if you use that as the mass in the KE formula, you get KE = .5 (4,198.7890 kg) (7174 m/s)^2 = 1.08048E11 J = 108000 MJ and KE = .5 (4,198.7890 kg)(7244 m/s)^2 = 1.101669E11 J = 110100 MJ. Only when doing that do I get KE change (108000 - 110100)MJ = -2100 MJ. Then I can get the example you showed me at the end of 2 * (-2100 MJ) / ( (7174 m/s)^2 - (7244 m/s)^2 = 4,161.4648 kg. I know its not exactly the same, but its close.
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Just looking at me example above is exactly what I have reasoned out on each attempt at this question, and was what I was trying to explain to you. I just do not see how there is not a randomly generated mass to answer this question. The mass would have to be something, right? Again, I may just be missing the obvious, but this question has me hung up. I just can't figure it out. I know the parts, but I do not know what I am missing.
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The phrase 'For the `mass kg mass of the satellite' includes `mass, which is the shorthand used in the 'source' problem for a randomly generated variable designated '`mass'. The program generated a random mass, but failed to display it in place of the designation '`mass'.
However the randomly generated mass was used in calculating the kinetic energies.
As you have inferred the mass used in the solution was about 4200 kg.
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