# Calculating Impact Force

1. Mar 19, 2013

### DynamicMenace

1. The problem statement, all variables and given/known data
This isn't for homework or anything like that, just something that happened to my mom around 2 years ago that I'm trying to calculate what forces she was subjected to.

She and my dad were walking the family dog (not that it's relevant, but I'm an adult and don't live at home) on a path right by their house that they do almost every day. It is a concrete path and people ride their bikes on it. This day she was hit by a biker traveling at high speed from behind and knocked to the ground. I am looking for what the force of impact was both when he hit her and, more importantly, when she hit the concrete.

She is 5'2" and weighs around 95 pounds. She estimated he weighed 200 pounds and was traveling at 20 miles per hour.

2. Relevant equations

I believe F = 1/2 m v2 / s is the correct formula, but this is where I am running into a snag. I'm not entirely sure that it is correct, and if it is, I don't really know what to do for the slow down distance, which is a huge part of the equation I gather.

3. The attempt at a solution

I've tried a few different things plugged into the slowdown distance, and just don't know if any of it is correct or if I am wildly off point. Second, what would be the best unit to convert or use to explain this in layman's terms?

Any and all help is appreciated, and if I can provide any more information, of course let me know!

2. Mar 19, 2013

### haruspex

There are many threads on this forum asking for how to calculate the force of an impact. The short answer is that you can't. You may be able to calculate the kinetic energy, and you may be able to calculate the impulse (change in momentum), but force is trickier. If you could study the impact microsecond by microsecond you would find that the force rises from zero to some maximum then decays away to zero again. If you plotted that as a graph of force against time, the area under the graph would be the impulse. If you knew the duration of the impact (which is pretty hard to know) you could calculate the average force, but it would not tell you the peak force, which is often more important.
Fwiw, I very much doubt the estimate of 20mph unless it was down a hill. 20kph perhaps. 200 pounds also sounds like exaggeration. Let's try 20kph and 80kg, with your mother at 43kg, stationary. The impact would have been mostly inelastic, so take them as coalescing. Speed after impact = 20*80/(80+43) kph = 3.61m/s. For your mother, that would have been like falling 3.612/2g = 0.67m onto a hard surface. The subsequent fall to the ground would have been a similar impact.