1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The energy of debris ejected from an asteroid impact

  1. Mar 5, 2014 #1
    I have been struggling with this problem. I'll greatly appreciate someone pointing me in the right direction. I think it's safe to assume the velocity of the impact is the Earth's escape velocity 11.1*10^3 m/s

    Here's the problem:

    Impacting objects will excavate a certain amount of debris material from a crater md and loft it into
    Earth's atmosphere to a height h. For an impacting object of mass mi, calculate how much debris mass md is lofted to an altitude h (where it will have zero velocity due to deceleration in Earth’s gravity). Assume that h << Rearth. Your answer will depend on mi, h and Rearth. For simplicity, assume the impactor comes in from straight up (along a radial line) and the debris is lofted straight out, also on a radial line. Consider h = 10 km, which is the altitude of the Earth’s jet streams. If debris reaches this altitude it will circulate globally. How much mass will an asteroid with density 2 g/cm^3 and diameter 1km be able to lift to a 10 km altitude?
     
  2. jcsd
  3. Mar 5, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Well, a realistic model would be way beyond the scope of this homework, so I guess you are supposed to calculate the maximal amount of material, based on the impact energy.

    It would be useful to know some context of the problem (in which course/class are you? What is the current topic?), but it looks like introductory physics.
     
  4. Mar 5, 2014 #3
    It's not supposed to be that realistic, hence the radial trajectories. The course is an intro astrophysics class, and the context of the question is asteroid impacts.

    If you consider it an intro problem, then please move it to the appropriate section (sorry, I'm new).

    Thanks.
     
  5. Mar 5, 2014 #4

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Would you be happy with a calculation where the kinetic energy of the asteroid is converted to potential energy of the debris? As if mi fell on a seesaw with md at the other end ?
     
  6. Mar 5, 2014 #5
    Sure, that sounds right. Although, wouldn't that be be kinetic energy being transferred from one body to the other?

    I figured the mass of the asteroid would be the same as the mass of the ejected debris, and the energy would be the same as well. Where I get stuck is how to make that energy dependent on the height h and Earth's radius. I'm thinking Earth's gravity would have factor in somewhere, since h is dependent on it. And I assume geometry will be involved, since both trajectories are just straight radial lines, but I just can't figure out how to do it. Your approach sounds like the right track
     
  7. Mar 5, 2014 #6

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If md = mi there is nothing to calculate any more.... The question - rephrased - is to calculate how much md you can lift 10 km with the kinetic energy in mi at 1.11 x 104 m/s. It is a rough upper limit, but probably not even all that bad.
     
  8. Mar 5, 2014 #7
    The average speed of asteroids is about 25 km/sec. That's more than 4x the kinetic energy of 11 km/sec.

    Chet
     
  9. Mar 5, 2014 #8
    @BvU Now that you put it this way it suddenly makes sense. Yes, then that is what I need! Thanks.
     
  10. Mar 5, 2014 #9
    Ok, so based on BvU's recommendation that I transfer kinetic energy to potential energy.

    Here is what I did:

    Ed = md*h*g = md*h*G*Mearth/Rearth^2 (g = GMearth/r^2)

    Ei = 0.5*mi*v^2 (v = escape velocity of Earth)

    Ed = Ei

    so I equate the two and solve for md and the answer depends on mi, h and Rearth, like the problem asked.

    Did I do it right?
     
  11. Mar 5, 2014 #10

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Looks good.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: The energy of debris ejected from an asteroid impact
  1. Asteroid impact speed (Replies: 8)

Loading...