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Momentum Principle Related to Velocity

  1. Mar 1, 2007 #1
    1. The problem statement, all variables and given/known data

    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


    2. Relevant equations

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

    3. 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.
     
  2. jcsd
  3. Mar 1, 2007 #2

    Doc Al

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    Staff: Mentor

    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.
     
  4. Mar 1, 2007 #3
    By momentum principle I mean DeltaP = Fnet*DeltaT
     
  5. Mar 1, 2007 #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.
     
  6. Mar 1, 2007 #5
    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.
     
  7. Mar 1, 2007 #6

    Doc Al

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    Call the speed "v" and express dP/dt in terms of it (along with other known variables).
     
  8. Mar 1, 2007 #7
    v= dr/dt I can find dr because I know the radius of orbit, but I have no way of finding dt.
     
  9. Mar 1, 2007 #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.
     
  10. Mar 1, 2007 #9
    I dont understand how you can express the period in terms of v if you don't know the time.
     
  11. Mar 1, 2007 #10
    Ok, I figured out the problem.

    v = sqrt(G*Mearth/r)
     
  12. Mar 2, 2007 #11

    Doc Al

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    Excellent.
     
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