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How do you calculate the amound of energy an asteroid has coming into Earth's atmos.?

  1. Jan 6, 2013 #1
    1. The problem statement, all variables and given/known data
    -- This is out of Rendezvous With Rama by Arthur C. Clarke
    You know it is 907184 kg and is going 50,000 m/s
    So how much energy does it have right before it hits the earth?
    2. Relevant equations

    Do I use Fg= Gm1m2/r^2 ?
    Ek=1/2mv^2?
    I have ΔE=1/2mv^2 written down as an equation to use as well.

    3. The attempt at a solution
    I think I'm supposed to calculate the potential energy at 2 different spots and find the ΔE, but I'm not sure.

    E=Gm1m2/r+1/2mv^2 would that work?
     
    Last edited: Jan 6, 2013
  2. jcsd
  3. Jan 6, 2013 #2

    haruspex

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    Re: How do you calculate the amound of energy an asteroid has coming into Earth's atm

    At any particular point it has both KE and PE. As it descends, PE decreases and KE increases by the same amount. At the point you describe the KE is given by Ek=1/2mv^2, but to know what the energy will be when it strikes Earth you also need to know how much PE it will lose in the remaining descent. So you need the altitude at the point where the speed is known.
     
  4. Jan 6, 2013 #3
    Re: How do you calculate the amound of energy an asteroid has coming into Earth's atm


    Okay, so then the equation would be E=EK+EP?
     
  5. Jan 6, 2013 #4

    haruspex

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    Re: How do you calculate the amound of energy an asteroid has coming into Earth's atm

    Depends what you mean by EP there. Write the equation in terms of four entities: Eki = KE at known initial point, Epi = PE at known initial point, Ekf = KE on collision, Epf = PE on collision.
     
  6. Jan 6, 2013 #5
    Re: How do you calculate the amound of energy an asteroid has coming into Earth's atm

    Yikes... you're confusing me.
    I guess what I'm asking is what steps would I do to get to my final equation?


    Would it be Efinal=Ekinetic+change of Epotential ?
     
    Last edited: Jan 6, 2013
  7. Jan 6, 2013 #6

    haruspex

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    Re: How do you calculate the amound of energy an asteroid has coming into Earth's atm

    Yes, provided (i) Efinal means the KE on impact, and (ii) you get the sign right on the change in potential.
     
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