# Unfortunate fall

1. Jan 8, 2005

### cepheid

Staff Emeritus
This isn't homework...I was just thinking through this rather morbid scenario and realised that I couldn't remember how to calculate the result I was looking for. The morbid scenario is person falling from a building of height h. How do you calculate the force exerted on the person by the ground when he/she hits it?

Obviously, it is easy enough to calculate the maximum velocity the person will achieve just before hitting the ground. From this, we can determine his or her change in momentum from mv_max to zero. But without knowing the time over which the force acts (very small, to be sure), how could we calculate the force of impact?

2. Jan 8, 2005

### rcgldr

Depends on a lot of factors, a lot of fat will reduce the g-forces. The brittle bones of an old person will just fracture right away. The soft bones of a baby would flex a bit more before breaking. Doing a belly flop would generate more g force than landing head first.

You could always visit rotten dot com for some gruesome pictures and use those as a guide.

So what started this, seeing Michael Jackson holding his kid out the window of a tall building?

Last edited: Jan 8, 2005
3. Jan 8, 2005

### cepheid

Staff Emeritus
No, it had nothing to do with Michael Jackson...although I did have the misfortune of watching a recent documentary on TV entitled "Michael Jackson's Face". The progression of his appearance was very disturbing, and also sad.

To get back on topic, I'm afraid I didn't understand your response. I agree that the effect of the force of impact would be different depending on the body type of the person falling, but that isn't what I was asking. All I wanted to know was how to calculate this force, which would depend only on the required change in momentum, and the time interval over which this had to occur. The final momentum just before impact, in turn, would depend only on the mass of the person (v_max would not vary from person to person). How, without knowing the time interval over which this would occur, could one perform this calculation?

Edit...upon a second reading, I see that you may also have been implying that the time over which the force would be exerted would depend on the body shape/softness etc, and without exact information, we could never calculate it. But, is there a more satisfactory response as to how to calculate it, in principle?

Sorry for the morbidness...it doesn't even have to be a person. We could even drop a ball...changing the problem from one involving an inelastic collision with the earth, to an elastic collision. To make things more general: the bottom line of what I'm asking is...how do you do collision problems in which an object, falling under the influence of gravity from an initial height h, hits the ground, especially how to find the impact force?

4. Jan 8, 2005

### dextercioby

Never mind the morbidity.It would have morbind if u had asked the surface distribition of the man's brain after the fall...
It is a collison problem.The question is not common,however.In the classical theory of collison,we're interested more in the velocity of particles after the collison.Why are we not generelly questioned about the force??Because the parameter on which our answer depends is almost impossible to determine,especially in plastic collisions.You have to find te time interval in which the momentum transfer takes place.That's not an easy task.We could only make rough estimations in the case of elastic collisions,but in this morbid scenario,it's really impossible.

Daniel.

5. Jan 8, 2005

### kirovman

Impossible without some real data I guess.

*evil grin*

I have only studied collisions without plasticity before, my physics degree only had a small introduction to mechanics, before occasionally using it again in nuclear physics, and various other modules, but nothing like that.

I imagine there is a lot of study into this kind of collision, people who design cars need to know what the force on someone is when their car hits someone I am sure, so they can try to increase their safety standards.
You can make some good approximations, or do some little mathematical tricks to get around the problem. It's not quantum uncertainty, or Higg's Boson stuff, it's classical mechanics.
Sorry I can't answer the question, but I'm just reasserting the hope that someone can answer you.

6. Jan 8, 2005

### pervect

Staff Emeritus
You need an estimate of the stopping distance. Then you can use the equation force*distance = 1/2 * m * v^2.

If you don't have an estimate of the stopping distance, you'd need to know the materials properties (young's modulus, etc) of the body and the ground to be able to calculate it.