Hypothetical Question Of Physics...

[Chipchopper]

Can it be explained in simple terms, the extent of impact of two vehicles in a head-on collision.

Here's my scenario:- car A & car B are travelling in opposite directions, both are doing 50 mph (no head winds).

Is the combined speed of both cars, doubled to result in a impact of a 100 mph ?.
Or would the result of the impact be the same as, car A running into, the stationary (spelling) car B, with is hand break off, and the force of impact resulting in 50 mph ?.

Thirdly, which one of Newtons laws, best explains this ?.

[interele]

It's the same as hitting a solid object at 50mph. Although the closing speed is 100mph the deceleration happens over twice the distance.

M

[Graham-W]

If both cars are the same weight it will be as if both cars hit an immovable object at 100mph. The closing speed of the two cars is 100 mph and Newtons second law is Force= Mass * Acceleration. In this case it's a sudden DE-celeration but that is the same as a negative acceleration. The force will be the mass of one car decelerating from 100mph to zero mph in a very short time.

[Clanad]

The now defunct TV program 'Mythbusters' here in the U.S., actually accomplished your hypothetical. See the results here:

http://scienceblogs.com/gregladen/2012/10/01/mythbusters-on-head-on-collisions/

And YouTube here:

[Graham-W]

I'm sorry. I stand corrected. interele is correct. See here: http://www.sciforums.com/threads/collision-physics-explanation-needed.104387/

[EDDIE51]

That answer is a bit misleading. In the case of 2 cars hitting head on at 50 mph the force to EACH CAR would be equal to hitting a solid object at 50 mph.
Both cars would be damaged to the same extent.
In the second case, hitting a stationary car, the hand break being off would make very little difference. The impact would still be very near the same as hitting a wall. This is because of inertia, the stationary car would not start to move forward fast enough to make more than an insignificant difference to the force of impact.

[EDDIE51]

^^ That was to interele , other answers were not there when I started typing.

[Togo]

Unless the cars are identical in weight and crumple zone technology, made with identical materials, and in the same state of repair, one of them is going to be compromised more than the other.

[Chipchopper]

Thank's Clanad,
The 'Mythbusters answered my question perfectly (I hadn't seen that episode before).

And thank's to all the other good answers!

[Khandro]

If one car was a Fiat 500 and the other was a Bently Mulsanne, I don't know which of Newton's law would apply, but the poor guy in the Fait would definitely experience sod's law.

[mibn2cweus]

All other factors being equal -

Two cars with same speed colliding head-on has the same result as each car hitting an immovable barrier at same speed.

If one car is not moving at the instant of colliding the result is same as each car travelling at half the speed of the moving car.

Much better to hit a parked car (preferably one with no occupants) than a head-on crash with a car moving in opposite direction.

[Old_Geezer]

I confess to having just learnt something. Seems pretty counterintuitive to me.

[Khandro]

It proves you've gotta get up early in the day if you want to try to outsmart old Isaac! His anagram went;

6a cc d ae 13e ff 7i 3l 9n 4o 4q rr 4s 8t 12u x

The solution;

Data aequatione quotcunque fluentes quantitates involvente, fluxiones invenire; et vice versa

Vladimir Arnold, a distinguished 20th-century mathematician and profound student of Newton's work, helpfully translates this as

"It is useful to solve differential equations."

or more expansively;

Analysis of motion by considering its smallest parts is a good thing. It allows you to determine the forces from the trajectories, or the trajectories from the forces.

[jim360]

Yes, it is a bit OG -- indeed on a first read of the question I would have probably said "yes" rather quickly and moved on without a second thought, and so been wrong. I suppose the point though is that while, at the instant before the impact, two cars doing 50mph in opposite directions is equivalent to one car doing 100mph, what matters once the impact begins is (kinetic) energy, rather than speed. The kinetic energy involved scales as the square of speed, and 100^2/(50^2+50^2) = 2, ie a 100mph car hitting a stationary car has twice as much kinetic energy as two 50mph cars hitting each other.

So a slightly better (if still probably naive) argument would suggest that the 100mph collision is about twice as destructive as the 2*50mph collision, and further that you'd have to have two cars travelling at about 70 mph head-on in order to try and replicate the effects of a 100mph-stationary collision.

This probably isn't quite right either, mind, but the counter-intuition at any rate is emerging from accidentally assuming that things always scale linearly.

[Old_Geezer]

That's a good way of picturing it. 100mph's worth of damage, but shared between 2 cars. They get 50mph's worth each.