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Momentum Principle Related to Velocity

  • Thread starter cowmoo32
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  • #1
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Homework Statement



You will need to use the Momentum Principle to do the first part of this problem, and the Energy Principle to do the second part.

A satellite of mass 2500 kg orbits the Earth in a circular orbit of radius of 8.3 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 1024 kg.
What is the speed of the satellite?
I have the 2nd part of the problem, so all I need is the momentum principle


Homework Equations



Pfinal = Pinitial + Fnet*DeltaT
GMm/r^2

The Attempt at a Solution


I'm not sure how to start this one. The directions say that I'm supposed to use the momentum principle, but I'm not given the speed of the satellite. I was thinking maybe the derivative form of the momentum principle and find the perpendicular component of dP/dT, but I'm not sure how long it takes for the satellite to go around th earth. I'm completely stuck.
 

Answers and Replies

  • #2
Doc Al
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I have no idea what you mean by the "momentum principle". If you mean conservation of momentum, I don't see how that is relevant.

Instead, apply Newton's 2nd law to the satellite, recognizing that its motion is circular.
 
  • #3
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By momentum principle I mean DeltaP = Fnet*DeltaT
 
  • #4
Doc Al
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OK, I see. Your initial thought was correct: Use F = dP/dt. (Note that this is another way of stating Newton's 2nd law.)

Use what you know (or should know) about circular motion to evaluate d(mv)/dt = m dv/dt.
 
  • #5
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Here's the problem I have with using dP/dt: In order to find the velocity, or the change in momentum, I need to know the time it takes for one rotation around the earth....that's why I didn't use that formula in the first place. v = dr/dt, but again, I don't have dt.
 
  • #6
Doc Al
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Call the speed "v" and express dP/dt in terms of it (along with other known variables).
 
  • #7
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v= dr/dt I can find dr because I know the radius of orbit, but I have no way of finding dt.
 
  • #8
Doc Al
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You can express the period (if you need it) in terms of v, since you know the radius of the orbit.
 
  • #9
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I dont understand how you can express the period in terms of v if you don't know the time.
 
  • #10
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Ok, I figured out the problem.

v = sqrt(G*Mearth/r)
 
  • #11
Doc Al
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Excellent.
 

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