Regarding the laws of physics.

[Starsky]

If two identical cars crash head on at 30 mph, the equivalent force felt by each vehicle is equal to the force felt by a 60 mph impact with a stationary vehicle (or thereabouts). The consequent damage to each vehicle should be roughly the same. My question is this - if one of the cars was doing 40 and the other 20 - which car would sustain the most damage? The reason I ask because I was in a crash yesterday and wondered whether the fact that my car sustained most of the damage would indicate that I was going faster or the other car? Any help much appreciated.

[Hamish]

The first part of the question is correct, and really answers, as much as is possible the second part. The total force is a result of the sum of the energy of the two veichals (assuming a head on collision) Therefore if everything is EXACTLY the same them the same result would be seen. Unfortunately in real life physics is more complicated and it becomes engineering. No two cars will be structurally the same as well had having the same mass distribution and smae coefficient of friction with the road. Also a real head on collision, ie both cars are EXACTLY head on AND neither move from a head on position during the collision is very very unlikely. Once the factors that the real world throws in are taken into account then the maths becomes much much much more comploicated and the distribution of damage impossible to tell quantitaively. A quallitative assessment might be possible for a crash investigator. Sorry this isn't what you wanted to hear.

Hamish

[lisaj]

Hamish is right: bear in mind that some cars are designed to crumple like paper - they look awful afterwards but at least you're alive: they've absorbed most of the collision force! The other car might not have been designed to crumple and yours might have been...

[darth vader]

I have a feeling the damage would be the same but the re-coil distances of each car would be different (i.e. they would end up in different places after the impact). I can't think of a mathematical/physics reason why though, just a gut feeling...... i feel the law of momentum has something to do with it...

[Starsky]

Thanks for the answers guys. I'll take comfort in the fact that my car crumpled more because of "better design". FYI, I was in a 99 Passat and the other car was a 97 Chrysler Neon. It was still driveable whilst mine is close (but not close enough unfortunately) to being an insurance write-off. Both my airbags went off whereas neither did in the Neon. Better to be safe than sorry, I suppose.....

[gazzawazza]

Just for your information Starsky, airbags only activate within certain constraints. For example, in a head on collision the front airbags will only deploy if the impact is within a range of 14 degrees from straight ahead, whilst side airbags should not activate at all.

[Squirrel]

I won't go into the derivation of the formula, but I always thought that Kinetic energy (joules) = �mv�. Taking the mass of each car to be 1kg, this gives the total Ek of 2 30m.p.h. cars to be 900J, whereas the Ek of one 60m.p.h. car is 1800J. (Ignore me if I'm writing rubbish here). For 40 and 20, the 40m.p.h. car has 800J, and therefore carries 80% of the kinetic energy. As for when the two cars crash, I imagine that whichever decelerates fastest would get the worst dents. I thought it would be worse for the slower car, personally, because it's being hit by a comparitively large momentum whereas the fast car is being hit by a comparitively small one. If that's true then there's not much to be said for obeying the speed limit. Then again I always confuse energy with momentum.