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Gforce on impact

  1. Jan 11, 2013 #1
    Ok, so this isn't exactly homework, but it seems the most appropriate spot to post this.

    A few days ago I (a 220 lb individual) hit an impact from a fall from 3 ft of my entire weight on a single toe against an unmovable object (tile floor)

    I'd like to know the gforce of that impact, assume I came to a full stop nearly immediately

    I'd also like to know the gforce of a 30 lb object impacting from 3 ft against a slightly padded object, quick stop though (for comparison with someone who thought I was out of line for getting an X-ray when I couldn't walk after for over a day, who used that as a line of reasoning object impacted a shoed foot in this scenario, initial scenario was a bare foot with all force against big toe)

    I appreciate any help calculating this that can be given.
     
  2. jcsd
  3. Jan 11, 2013 #2

    haruspex

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    We get this question all the time, in different guises. The short answer is that you cannot know without further, detailed information.
    You do know the momentum change to be undergone, but that is the integral of force over time. The longer the time the impact is spread over, the lower the peak force can be. An instant stop would imply an infinite force, which clearly never happens.
    In the case of your toe, your toe would have come to a stop in much less time than the rest of you. Suppose the whole process took half a second, and the force rose linearly to a peak then fell away linearly at the same rate to 1000N over that time. Your momentum change was 100kg * √(2*9.8) m/s = 443 kg m/s. If I've calculated correctly, that gives a peak of 2358N, or 2.4g.
     
  4. Jan 11, 2013 #3
    Ah. I know when it happened the impact seemed to be an instant stop and the damage to the foot was enough the doc had to double check the X-rays for a break after looking at the bruising. It was a curiosity what the gforce it took to cause that level of bruising since it was enough that made me unable to walk for a day.

    I thank you for the help :) I know exact wouldn't have been possible without a lot of precise measurements anyway and that's not something I'm willing to recreate and get those kind of measurements for what amounts to be curiosity. (plus next time I may not be so lucky that it doesn't break lol)
     
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