Forces experienced while falling out a window?

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Main Question or Discussion Point

Recently I read an article in the newspaper (yes, someone still reads them) of someone who committed suicide by jumping out a window of a 7 story building. That got me to wondering how much "force" he experienced at the moment of impact. (I don't know if force is the metric I'm looking for, hence the quotation marks.)

Assuming he weighed 100 kg, how much force would he have experienced when he hit the ground? Let's say 7 stories is 70 feet, or 21.336 meters. I know that F = ma, but that just results in 980 N of force. I understand that there are numerous other factors, so let's say he hit his head and that the top had an area of 0.5 ft^2 (0.04645 m^2). Also assume that the impact was near instantaneous, so perhaps the duration of impact was 1 microsecond. I know that there's the issue of linear and rotational motion, but I want to ignore that.

I don't know what other factors would have influenced the "force." Kinetic energy? Momentum? I know it's a weird question, but I've been thinking for it all day and don't know how to approach it.
 

Answers and Replies

  • #2
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Fnet = ma
= change in momentum/time of impact
and
Fnet(downwards) = weight - force by ground

hence we need to make an estimate for the speed with with he hits floor and an estimae for the time of impact.
 
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I don’t know if any of this helps and ignoring for the moment the size of the head etc., Presuming that the body is falling from rest, its initial KE is zero, when it hits the ground PE = zero (no height hence no PE) . Taking initial PE = final KE. mgh = ½ mv2. The kinetic energy would be equal to 100 Kg x 9.8 x 21.33 = 50 x v2 or 20903.4 = 50 x 418. Therefore velocity = 20.44m/sec and kinetic energy = 20903.4 Joules. Exactly what impact this would have on a body, especially if it hits head first, is anyone’s guess.
 
  • #4
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Having an estimate for the velocity with which he hits the ground, one can now find the rate of change of momentum given an estimate for the time of impact.
 
  • #5
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Having an estimate for the velocity with which he hits the ground, one can now find the rate of change of momentum given an estimate for the time of impact.
By time of impact, do you mean duration of impact? Since we're dealing with concrete, I assume that the impact is near instantaneous, right? So t could feasibly be, say, one millisecond?

So since F = ma = p/t, p = ma*t or 980 N * 0.001 s = 0.98 kg*m/s?

I also still don't know what killed him. I hate sucking at physics...
 
  • #6
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By time of impact, do you mean duration of impact? Since we're dealing with concrete, I assume that the impact is near instantaneous, right? So t could feasibly be, say, one millisecond?

So since F = ma = p/t, p = ma*t or 980 N * 0.001 s = 0.98 kg*m/s?

I also still don't know what killed him. I hate sucking at physics...
That's the biggest unknown here, and is probably what is confusing you: the duration of impact. You say a millisecond, I say a hundredth of a second, and someone else will say something else. Ultimately we are all guessing, and we all get answers orders of magnitude deifferent. Relistically it depends on what the person hits, how he hits it, how his body reacts, and who knows how many other factors that most likely need to be found experimentally. And even then the answers will vary widely.

Surely there is an accepted "estimate" for hitting concrete, but you need to find it if you want to solve this. Shooting from the hip at the duration of impact, you might as well skip the calculations and just take a guess at the impact force.
 
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I guess if he hits on the head, he is dead!
 
  • #8
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That's the biggest unknown here, and is probably what is confusing you: the duration of impact. You say a millisecond, I say a hundredth of a second, and someone else will say something else. Ultimately we are all guessing, and we all get answers orders of magnitude deifferent. Relistically it depends on what the person hits, how he hits it, how his body reacts, and who knows how many other factors that most likely need to be found experimentally. And even then the answers will vary widely.

Surely there is an accepted "estimate" for hitting concrete, but you need to find it if you want to solve this. Shooting from the hip at the duration of impact, you might as well skip the calculations and just take a guess at the impact force.
I suppose you're right. Although I completely forgot that F = ma = p/t... for the longest time I simply had p = mv in my head. I'll do some digging around tonight and see if there is some accepted "estimate."

@McQueen: Haha I guess so. At the end of the article they mentioned someone going to start a fundraiser to install protective screens in the upper floor windows, so I guess it's not the first time. Maybe 7 stories is sufficiently high enough to cause enough internal damage to result in death?
 

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