[chris (OP)]

In terms of impact, what's the worst smash to be in, one involving a single vehicle running headlong into a wall at 100mph, or two (let's regard them as identical) vehicles travelling at the same speed (100mph) but in opposite directions and hitting each other head-on?

[chiralSPO]

If the cars are identical, and hitting each other head on with a relative velocity of 200 mph, I would say that should be much worse than one car hitting an un-moveable wall at 100 mph. If the closing speeds of both cases were the same, then I think the un-movable wall would be somewhat worse because the wall won't take any of the momentum or kinetic energy. If the wall can bend/break then probably about the same as hitting a car.

[Blame]

We do have to make a few assumptions here. First that the wall is and remains perfectly flat with no give. Second that all 3 cars are identical and the two in collision meet exactly head on.

The result, in theory, will be 3 identical wrecks although I doubt the experiment could ever be set up so precisely. So the two cars trashed has to be worse than one.

[Blame]

chiralSPO

Think it through. Think of 2 two identical cars hitting the wall from each side at the same time. The wall doesn't move.

Now do it again with a wall made from a sheet of paper. As the forces are identical on each side the wall doesn't move. The damage will be the same because in both cases because the cars hit an un-moving wall.

 So how much more damage will the cars suffer if you take the paper away?

[Bored chemist]

The two-car case has twice the kinetic energy, but it shares that energy between two cars so the damage is that same as for 1 car hitting an (immovable) wall.
If the wall has any "give" then some energy is lost to damaging the wall, so less would be available to damage the car.

[Blame]

Board Chemist

Thanks. A much clearer explanation.

[syhprum]

The two car case has 4 times the energy (shared between two cars).
E=MV^2/2 the velocities are low compared to c that we do not have to consider SR.

[chris (OP)]

Not quite.

KE = 1/2mv²

Let's take two notional identical trucks; each weighs 100kg and they are travelling at 10 m/s in opposite directions.

KE of first vehicle = 0.5 x 100 x (10 x 10) = 5,000J

KE of second vehicle = 0.5 x 100 x (-10 x -10) = 5,000J  * Note velocity is negative because direction is opposite to vehicle 1

Combined KE is vehicle 1 plus vehicle 2  = 10,000J or twice the KE of one vehicle alone. Not four times.

As Bored Chemist then points out, the KE is shared between two vehicles involved if they collide. So the net KE per vehicle smashing is the same as if one vehicle alone smashed into a wall.

However, the human cost of a multi-vehicle smash is likely to be much higher...

[SeanB]

As well consider that it is rare for a vehicle to impact a wall directly, generally you hit along an angle so the energy is dispersed somewhat over time, leading to a lower deceleration of the vehicle frame and thus a lower differential ( time is longer to dissipate the energy) between the notionally rigid but deforming vehicle frame and the free to move occupants of the vehicle.

Thus the trauma forces are lower than the head on collision, where you pretty much have only the time it takes the crumple zones to deform as the deceleration time. Whacking a wall at 100kph and you might survive after the car finishes shredding parts for 100m down the highway. Hitting another vehicle head on at 100kph you all die. Airbags and other secondary safety systems ( seatbelt is the primary SRS, the others are ineffective if it is not on) might help, but are at the point where they might only mean you are either paralysed or dead.

[Bored chemist]

The two car case has 4 times the energy (shared between two cars).

No, Twice the KE.