Head-on Collision Physics

I have a knucklehead friend I am unable to convince of a fairly simple physics problem. He contends if two cars of equal mass (discounting crumple zones and the like) both traveling 35 mph meet head-on, the resulting collision is multiplied to a 70 mph crash. I told him it’s the speed of stopping that’s important, that this scenario is no different than had one car traveling 35 mph run into a immovable brick wall — the car goes from 35 to zero near-instantaneously. He disagrees, in the face of logic, and I can suffer his foolishness no longer. I’m long past my days of high school physics, and can’t quote the various laws which lay waste to his folly. Any takers?

I must be a knucklehead as well. Two cars crashing head-on at 35 mph is like one crashing into a wall at 70. See, both vehicles have what’s called inertia which may be calculated by the speed and the weight of each vehicle. This inertia is dissipated at the moment of the crash, but not willingly because objects in motion tend to stay in motion.

Believe me. If you get into an accident, hit a parked car instead of one approaching you at the same speed you are traveling.

Sure, but the parked car moves. The wall doesn’t. It’s the same as a counteveiling force. Clearly, you would not suffer as great of force if you were traveling 45 mph and your doppelganger auto was moving 35. You would continue to move, albeit significantly slower. Your poor schnook twin, however, would suffer even greater force than had he simply run into a brick wall, as his momentum was even more violently made retrograde. But I’m still looking for the physics of this.

If you hit a brick wall (assuming it stays in one place and doesn’t break), it exerts the same force back to you as you put upon it.
If you hit a car coming toward you, while you exert force on it, it exerts the same force back at you (like the brick wall) and also more force bacause its moving (your car is now like the brick wall).
I know that isn’t very well explained, but bascically, I agree with TC Burnett - hit a stationary object or one that is moving in the same direction as you.

But it exerts no greater force than your car does on it. Cancellation of momentum here. Here’s what was said in Scientific American on the subject. It bolsters my theory, but doesn’t give the theorom. http://www.sciam.com/askexpert/physics/physics27.html

Even the Director of the Center for Transportation Analysis at Oak Ridge National Laboratory gets this one wrong, it appears.

Bigtrout… sorry man, but your friend is not the knucklehead here.

With your idea of Physics, you say that it is the stopping force that matters. Since one car was going 35 mph and suddenly stopped to 0, that is where all the damage and force comes from. You say that it does not matter if he hit a wall or a car coming at him… he was still going 35 and slowed to 0 almost instantly.

Think for a second about the wall… do you think that the wall somehow does not feel the car crashing into it because the wall started at 0 and stayed at 0 it was uneffected and felt no force???

Ok so you say a wall feels nothing, it is just a wall. Ok if you were standing against that wall and a car going 35 mph hit you, you would definately feel the momentum of that car. You would feel it right before you got squished. Why would you think that because you started at 0 and then stayed at 0 that you would feel nothing?

Now… lets secure that wall, and you standing against it, to the hood of another car going 35 mph. You are now traveling 35 mph toward a car that is coming 35 mph toward you. Your friend is correct in saying that you would feel like the car coming at you was going 70 mph. Why? It is relative. The other car, relative to YOU, IS going 70 mph. The car you are attached to, relative to you, is not moving at all. So it would be like you standing against a stationary brick wall and getting squished by a car going 70.

And relative to me the observer… I just see some fool getting squished between to cars going about 35 mph each. Poor fella.

BigTrout is in fact correct.
if you hit the other car head on, both cars will come to a complete stop ( in theory with perfect symmetry, in practice things aren’t perfectly symetric and the cars hit slightly off center, etc., etc…)
the impulse force on the car required to bring it to a complete stop is the same and it doesnn’t matter if it was provided by another car in a head on or a brick wall.
if you hit a stationary car (of the same mass) then both cars are moving at half the original speed after the collision, and that would be equivilent to hitting a brickwall at half the speed.
a physicist

Thank you, Luckie. Now can you give a bit more detail in the realm of physics? It would be greatly appreciated.

bigtrout is right, the other trout is wrong.

I can see this needs more explanation…OK, if we go with your theory BigTrout (and luckie), a bat will interact with a baseball with the same force whether the bat is swung or not. Or for that matter, at no matter what the speed of the baseball. No offense to the physicists here, but if you compare hiting a wall in a car from 35 mph and then hiting an oncoming car (closing speed 70 mph), I guarantee that your car will stop faster by hitting the oncoming car. Look. Hit yourself in the head with a hammer, only moderately hard. Then double the speed of the swing. Is the answer becoming clear yet?

Since about half the people in this thread are wrong already (whichever way the answer actually is) I can go ahead and post my take on it, without standing out. I think, Bigtrout, that you are right, but only because you don’t know what you’re saying. Specifically, there is no such thing as “a[n] immovable brick wall”, one which no Force can accelerate or deform. In real life, though, that’s ridiculous. If a car smashes into a wall, it’s going to give a certain amount. This amount may not be much for the wall, but it’s a significant amount for the car. So, if a car going 35MPH crashes into a real life wall, it’s going to feel less of an impact than if it crashed into a car going 35MPH in the opposite direction.

The force of the collision is determined by what is called the impulse. The impulse, in simple terms, is defined as the change in momentum per change in time. In more complex terms, the average force exerted on an object is equal to the integral of the derivative of the momentum with respect to time:

F(avg) = (integral) dp / dt

What this basically means is this: In a head on collison, the net momentum of both cars will be reduced to zero. How quickly it is reduced determines the magnitude of the force. If both cars have the same mass and are travelling at the same speed (thus, have the same momentum), then the force on each car will be the same as if either had struck a non-moving object. In either case, the time increment is very small, leading to a very large force (and, consequently, the work done on your car and you).

Oh Bigtrout I just read that link…

Here is what is going on. Your original OP mentioned “the resulting collision”.

The man in the link is talking about a person inside one of the cars. We he hits something going 35 mph and suddenly stops, he exerts 35 mph worth of force on the windshield… or hopefully the seatbelt. His collision, do to his inertia is 35 mph against his steering wheel. If he hits something that gives then he will slow down more and not break the force of friection holding him in the seat and therefore will not hit his steering wheel. So of course it is best to slow gradually from 35 mph, not instantly.

What does this mean? It means, you and your friend can both be right depending on the specifics of the question. If you are talking about the total collision of two cars going 35 hitting each other being the same as 1 car going 70 and hitting a wall-that is correct. Your friend wins.
But if you are asking “Which is better to the driver?” Then you are right by saying it doesnt matter because he still hits his dashboard at 35mph, whether he hits a wall or another car coming at him…

When the poor guy’s car hits the other and stops instantly, the man is no longer connected to his car and he is not part of that total collision anymore, he conitiues to go 35mph himself until he hits something. That is why it does not matter to HIM what he hits. But it still matters to the poor car, or the poor sap CONNECTED to a wall on the hood of the car.
Hope this helps…

true, most any real object will have SOME give. the term brickwall is frequently used for a abstract that has no give, but if you have a giant block of reinforced concrete ( or hardened steel) that weighs much more than the car in question, then the difference between the reality and the abstraction will be negligible.
BigTrout: I don’t know how you can convince said knuckleheaded friend…

Sorry, Bear, I don’t buy into the addition of force theory. And I only used the Scientific American site to point out that it also debunked the 1+1 force theory, if you read carefully. I’m not concerned with the nuances of passenger effects here. What’s important, as noted in the threads, is how fast you stop. Hit a wall or hit an equal mass moving the same speed, the effect is the same.

bear said:
“If you are talking about the total collision of two cars going 35 hitting each other being the same as 1 car going 70 and hitting a wall-that is correct. Your friend wins.”

sorry, that is still incorrect.

let me toss this thought in:
bigtrout: point out to your friend that , while the 2 cars going head on at 35mph is NOT equivilent to hitting a brick wall at 70mph, it IS equivilent to hitting a stationary car at 70mph (that is a simple change of refernce frames). clearly hitting a stationary car at 70 is not nearly as bad as hitting a brick wall at 70! in fact , it is like hitting a brick wall at 35 (QED).
if he still doesn’t get it after thinking about that, give it up as a hopeless case.

He IS NOT debinking the addition of forces! There is something called the conservation of momentum.
If you put a force probe on the bumber of the car, you would get the same data from both collisions.
The writer in the article is talking about the effect on the driver.

Read your last post. I see what you mean and I will let you answer things for now on :slight_smile:

I can’t provide any further input. But I know who can.

The National Institute for Highway Safety:


The National Transportation and Safety Board:

Of course, we can always ask for help from Above.