# Physics of a car crash

1. Aug 5, 2007

### Darquis

1. The problem statement, all variables and given/known data
You're in a car, and you see a car coming at you in the opposite direction. Assume that both cars are identical in all matters including velocity and mass (neither given). To your left and right are a brick wall, you will hit this head on if you swerve. Is it better to swerve, do nothing, accelerate or hit the brakes?

2. Relevant equations

J=Ft (Impulse)
Conservation of momentum
Kinetic energy (maybe/)

3. The attempt at a solution

I know that the longer I am in contact with what I hit while still in motion, the longer it takes to transmit the resulting force back to me/my vehicle.

If I hit the wall, best case scenario is I stop right there, because the force is going to act quickly, and whatever momentum I have is going to be balanced by the impulse. If I go backwards, that impulse increases (as I now have a negative momentum, assuming my direction of travel to be the positive), which increases the force and possibly decreases the time.

Conservation of momentum leads me to believe if I crash head on into that other car, which will have the same momentum as me, it will be very similar to hitting that brick wall, assuming our cars don't rebound.

I've been using 20 m/s as velocity and 1000 kg for the car's mass, as both seemed reasonable as far as the problem went, but really they can be anything. Any ideas?

2. Aug 5, 2007

### Mindscrape

Well, the two keys here are momentum and impulse. If you are traveling slower then you will have less momentum. Force is related to momentum by F = dp/dt (change in momentum over change in time), so by lowering your momentum you are also lowering your force and impulse. You obviously can't change your mass, so you want to change the other part of momentum.

Items of discretion come from Newton's 3rd law, and how much deceleration both cars can do. If the other car does not decelerate then you will not want to take your chances hitting it (why?). Think about a real life scenario, would you rather hit something that is stationary, or something that is coming towards you at 30m/s?

3. Aug 5, 2007

### Darquis

So there'd be double the force acting on me, if we both kept our velocity the same, right? Which means it'd be worse in terms of force on my car if I tried speeding up (although by conservation of momentum, I'd be keeping my direction at least..but suffer a greater overall loss in momentum/velocity).

That makes sense enough to me, thanks. I'd also like to back up my answer with some numbers..if I use the equation J=Ft, what's a typical t for a collision? 1 second? .1 second? less?

4. Aug 6, 2007

### Mindscrape

Right. Given that the other car does not apply the breaks you are better off running into the wall. The best thing to do would be apply the breaks and hit the wall. In real life, you would probably want to hit him because he would apply the breaks too, and his car will have more give than the wall.

Cars these days are specially manufactured so that they have very long impulse times, with the idea of total the car and not the person. I'm not so sure, but I think that a half a second to a second might reasonable.

5. Aug 6, 2007

### andrevdh

The factor that determines the damage sustained is the magnitude of the deceleration - impulse takes both the force and time interval into consideration. One can obtain the same impulse by "distributing" the force over a longer time, that is the function of air cushions. One need to minimize the amount of sustained g's in an accident. Running into a (sturdy) brick wall brings you to an immediate stop - very large g's are involved. Colliding into another car effectively doubles the length of the crumple section of a single car. That is it is decelarated over a longer length.

Last edited: Aug 6, 2007