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Superman and the Kinetic Theory of Gases

  1. Apr 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Superman leaps in front of Lois Lane to save her from a volley of bullets. In a 1-minute interval, and automatic weapon fires 150 bullets, each of mass 8.0g, at 400 m/s. The bullets strike his mighty chest, which has an area of 0.75 m2. Find the average force exerted on Superman's chest if the bullets bounce back after an elastic, head-on collision.


    2. Relevant equations

    Kinetic Theory of Gases: P = [tex]\frac{2}{3}[/tex]([tex]\frac{N}{V}[/tex])(.5mv^2)

    where .5mv^2 is the average kinetic energy per molecule.


    3. The attempt at a solution
    After substituting values into the Kinetic Theory of Gases:

    P = [tex]\frac{2}{3}[/tex]([tex]\frac{N}{V}[/tex])(.5mv^2)

    P = (2/3)(150 bullets/V)(.598.0g)(400m/s)^2

    If V = 0.75m^2 * 1m = .75m^3, then P = 8.53 * 10^7 Pa.

    However, the answer in the textbook is 16N, I'm just not sure if:
    1. V (described above) is accurate.
    2. There is an equation to relate work and pressure. (Note: This is a algebra-based course.)
     
  2. jcsd
  3. Apr 18, 2009 #2
    This question can just as easily be solved by considering it kinematically as it can through a kinetic theory of gases perspective. Anyways, basically the jist of it is that, for each bullet, superman has to change its momentum by 2mv (mv to stop is and another mv to get it going back in the opposite direction at the same speed). Over the course of a minute he does this 150 times. so the total force divided by the total time
     
  4. Apr 18, 2009 #3
    Well, I thought about solving it this way, but my professor wants me to relate these problems to thermal physics :(

    Any help?
     
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