# Two cars head on at 50mph

by AJ_2010
Tags: brick wall
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 Quote by cabraham But if another car is approaching at 50 mph, the relative speed is 100 mph, meaning you'll have less time to slow down before impact.
Only if the other guy doesn't hit the brakes too.

 Quote by boneh3ad This isn't true either. Two vehicles moving at 50 mph will again, have 2E energy distributed between the two cars. That means that each car dissipates E amount of energy. If you have a stationary car and a 100 mph car, the total energy is 4E and the mass is 2M, so each car is dissipating 2E. That is going to be a much worse crash. To compare the head on collision to someone hitting a stationary car, the moving car would have to be moving at about 70 mph (50$\sqrt{2}$).
As long as we're neglecting friction between the cars and the ground, it's pretty obvious that velocities 50 and -50 (relative to the ground) are equivalent to 0 and 100. In both cases, the velocities are 50 and -50 in the center-of-mass frame, where the cars will eventually come to rest.

 Quote by boneh3ad Apologies if the LaTeX is messed up. This site always acts so goofy when it translates it...
You need to refresh and resend after each preview. It's not supposed to be that way, but no one knows what's causing it or how to solve it.
P: 2,467
 Quote by boneh3ad This isn't true either. Two vehicles moving at 50 mph will again, have 2E energy distributed between the two cars. That means that each car dissipates E amount of energy. If you have a stationary car and a 100 mph car, the total energy is 4E and the mass is 2M, so each car is dissipating 2E. That is going to be a much worse crash. To compare the head on collision to someone hitting a stationary car, the moving car would have to be moving at about 70 mph (50$\sqrt{2}$). Apologies if the LaTeX is messed up. This site always acts so goofy when it translates it...
Wrong. Final velocity of a 100mph car in a collision with stationary one is 50mph, not 0mph. Both the energy dissipation and momentum transfer are identical to 50mph head-on collision.

Not to mention the fact that this is a simple coordinate system transformation.
 PF Gold P: 10,766 The TOTAL energy that must be dissapated from two cars hitting head on at 50 MPH each will be equal to a crash of 100 MPH vs a stationary object. However, since both cars are designed to crumple and such, each equally absorbs half the energy of the collision, which is equal to a 50 MPH crash against a totally solid object which absorbs 0 energy. Rarely do two identical cars hit each other head on, so in the real world its a bit more complicated. (Such as semi's vs Mini Coopers) This is why they put those barrels of water or whatnot on many exits, so that the barrels absorb and dissipate energy over a greater distance than, say, a guard rail post, thus making the accident much less severe. Decelerating over a greater distance makes the accident much less traumatic for the passengers.
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 Quote by K^2 Not to mention the fact that this is a simple coordinate system transformation.
That isn't what makes what I said wrong.

 Quote by K^2 Wrong. Final velocity of a 100mph car in a collision with stationary one is 50mph, not 0mph. Both the energy dissipation and momentum transfer are identical to 50mph head-on collision.
That is.

 Quote by Drakkith The TOTAL energy that must be dissapated from two cars hitting head on at 50 MPH each will be equal to a crash of 100 MPH vs a stationary object.
Only if that object is not permanently stationary. In the case of the wall, where no matter what you do the wall won't move, this claim is no longer valid.
 Sci Advisor P: 2,467 Invariance under coordinate system transformation already tells me the statement has to be wrong. Damage can't depend on such a transformation. Analysis of final kinetic energy simply tells me exactly what is wrong with the statement.
P: 1,408
 Quote by K^2 Invariance under coordinate system transformation already tells me the statement has to be wrong. Damage can't depend on such a transformation. Analysis of final kinetic energy simply tells me exactly what is wrong with the statement.
It was a big red flag, sure, but it wasn't what was actually wrong with my statement. The problem was I overlooked the fact that the hulking mess that is left over after such a crash would not be stationary.

But now I am just arguing semantics so I will just stop, because that is silly.
 P: 25 I had a strong suspicion I was on the right line of thinking (even though my description of such may not have been the best ;) ). So to summarise (on a basic level): Sitting in a car travelling at 100mph crashing into an immovable wall is much worse than sitting in a car crashing into another car also doing 50mph head-on.
 Sci Advisor HW Helper Thanks PF Gold P: 26,107 hi angela25! welcome to pf! best thing to do (now you're here ) is to show us some problems that you've tried … go to the appropriate homework forum, click on the "NEW TOPIC" button, show us your full calculations, and then we'll see what went wrong, and we'll know how to help!
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 Quote by AJ_2010 So to summarise (on a basic level): Sitting in a car travelling at 100mph crashing into an immovable wall is much worse than sitting in a car crashing into another car also doing 50mph head-on.
Correct. Though, you probably wouldn't survive either.
 P: 25 True :) Although part of my line of work is to do with road accident data, (just the database side of things). But it would surprise you the number of high speed accidents with modern cars that people walk away from without as much as a scratch.
 Sci Advisor P: 2,467 If 50mph collision isn't quite head on, you have a descent chance. But surviving a perfect head-on would be near miraculous. Still, if the car crumples just perfectly, we are talking about 10g-15g, and that is technically survivable. There are just way too many things to go wrong.
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Mythbusters ? Adam Savage is so cool :P
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 Quote by AJ_2010 So to summarise (on a basic level): Sitting in a car travelling at 100mph crashing into an immovable wall is much worse than sitting in a car crashing into another car also doing 50mph head-on.
If the situation is perfectly symmetrical (one car being the mirror image of the other and the collision being exactly head-on), there can't be any difference at all. In the real world, the situation is never perfectly symmetrical. If the collision isn't exactly head on, the driver won't accelerate as much, and is less likely to get crushed between the front and rear of his own car. Even the fact that the driver of the other car isn't sitting directly in front of him improves his situation somewhat.
P: 25
 Quote by Fredrik If the situation is perfectly symmetrical (one car being the mirror image of the other and the collision being exactly head-on), there can't be any difference at all. In the real world, the situation is never perfectly symmetrical. If the collision isn't exactly head on, the driver won't accelerate as much, and is less likely to get crushed between the front and rear of his own car. Even the fact that the driver of the other car isn't sitting directly in front of him improves his situation somewhat.
But we've already established that there is a difference.
A person in a car decelerating from 50mph to 0 is very much different than a person in a car decelerating from 100mph to 0 (in a crash situation).
The energy from hitting a stationary wall at 100mph is totally taken up by the car. Therefore, yes the crumple zone is larger, but a crumple zone is not linear in terms of force/deformation. And therefore deceleration increases dramatically in comparison to lower speed crashes.

With a head on, both travelling at 50mph, the crumple zone of BOTH cars absorb each speed of 50mph. Resulting in reduced acceleration at this lower speed. (Crumple zone smaller than at 100mph yes, but also less force required/involved which in turn equals less deceleration).

As the driver is connected to the car's deceleration in terms of seat-belt (and anything in front of him/her that makes contact ie.dashboard etc, the forces on the driver can be looked at as being relative to those that are on the car.
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 Quote by AJ_2010 But we've already established that there is a difference.
I see now that you were comparing driving into a wall at 100 mph with a head-on collision between two cars both doing 50 mph. When I wrote the answer, I was somehow thinking of the car hitting the wall going 50 (the same speed as the two cars hitting each other). I guess I didn't think about what I was actually reading. Now that I am, I don't see why anyone would want to compare 100 mph into a wall with 50 mph head on. The relevant comparison is between 50 mph into a wall and 50 mph head on. My answer is correct for that comparison, but obviously incorrect if you double the speed of the car going into the wall.
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 Quote by Fredrik I don't see why anyone would want to compare 100 mph into a wall with 50 mph head on.

The police and the media seem to do it all the time.
This was one of the reasons I asked this question. Just to put my mind straight on the reasoning side of things.

Road safety is a big issue in the UK (and rightly so), but there is a constant pushing of big numbers relating to speed.
In my line of work I often use facts/figures/information from the accident database and speed is not ranked very high at all in terms of cause factor for injury accidents.

But most of our public tax money is aimed at reducing speeds on the road. And as such the media/police/politicians etc. always seem to push big numbers when referring to speed to cause 'shock' for use of a better word. (Well, this is my interpretation of events anyway).

Targeting speed is, as we all know, also a form of 'revenue' and generally the cheapest so called 'solution' to a 'black spot'.

Whether people agree with the above or not I'd just like to point out that its just personal opinion formed from work experience.

:)
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 Quote by AJ_2010 Targeting speed is, as we all know, also a form of 'revenue' and generally the cheapest so called 'solution' to a 'black spot'.
According to the sources I've seen: for a given road, a lower speed limit leads to fewer deaths and less emissions.

Why? Less kinetic energy involved and less energy dissipation per unit distance.
P: 154
 Quote by torquil According to the sources I've seen: for a given road, a lower speed limit leads to fewer deaths and less emissions. Why? Less kinetic energy involved and less energy dissipation per unit distance.
However, it could be argued that since cars have a lower fuel efficiency at lower speeds it is likely that more HARMFUL Carbon Monoxide might be released.

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