Tale of two cars (Physics question)

[Trinopus]

Thank you, all y'all, for this thread! I've learned stuff from it!

I had always thought that momentum, like energy, could be "lost" -- i.e., converted to other forms. Now I *think* I've learned better!

If I brake my car, my kinetic energy is (in part) converted to heat energy.

But my momentum is simply transferred to the earth as a whole. Is that right? If I'm travelling eastward, I speed up the earth's rotation (by a tiny amount!) If I'm travelling westward, I slow it down. If I'm going north or south, I actually alter the earth's axial tilt... Yeah, so microscopically that no one will ever measure it, but enough to "balance the books" and make the equations all sum to zero.

Er...is that right?

[Irishman]

Mostly right.

If traveling eastward, you are traveling into the Sun. The Earth rotates opposite of what you see the Sun do. Ergo, traveling eastward, you are actually slowing Earth's rotation, and traveling westward you are speeding it up.

[ZenBeam]

No, I think Trinopus has it right, if I understand what he's saying correctly. If he's braking while traveling East, he's transferring momentum into Earth's rotation (where "Earth" doesn't include him or his car ), speeding it up ever so slightly. Of course, to initially accelerate in the Eastward direction, he had to slow the Earth's rotation down first.

[Irishman]

Ah, yes, applying the brakes works backwards from the wheels pushing to drive. I guess I missed that he meant braking, vs driving.

[Trinopus]

Oops, yes, sorry, unclear: braking.

Again, for me, the eye-opener was that, unlike energy, momentum can't be converted into other forms. I can "throw away" lots of energy in the form of heat, but I can't do that with momentum.

(I guess I always thought it was just some kind of analogue of energy!)

[The Niply Elder]

As an engineer, I have to kind of agree with westom. Somewhat.

Since the OP asked about colliding cars, it's not a simple thought experiment. Basic equations on conservation of momentum will only get you rough answers. If the OP meant to ask this as a thought experiment, then he should have used colliding billiard balls.

The key to the debacle here are secondary collisions. The only way to predict these is through simulation. YouTube LS-DYNA for some cool car crash simulations. The pros run thousands of simulations, testing many variables: different speeds, different masses, different car models, different collision angles, different bumper heights, different coefficients of friction, heck the list is long. All these results are aggregated in huge Monte Carlo simulations, and the specific shape and design of the structural components are driven to satisfy the greatest test cases. I read somewhere that Mercedes Benz test crashed 50000 cars or so. The amount of crash simulations must number in the hundreds of millions. And the real crashes are used to verify their simulation models.

Anyway, to summarize, from an engineering perspective, as posed by the OP, no: the two cases are not the same, and the 100kmh car will release more energy and be dissipated in a different way with a higher resulting structural damage.

[Irishman]

Niply, it's all about assumptions. You're assuming "collision" = "real world car crash", which of course has to take in all those considerations of how each car is manufactured, and secondary results after the primary collision.

But the OP asked a basic physics 101 question that is answered with delta KE and conservation of momentum. Here is part of his post:

Pardon the ignorance. I really should know the answer to this, but it's been a long time.

That suggests he is trying to remember what he learned in school, not delve into a high fidelity crash study analysis to design a better automobile. So the assumption most of us have made is that is the answer he wants. I've posted links to those kinds of problems.

[Cheesesteak]

The other issue is that the summarized version glosses over the fact that the Car vs. Car interactions are identical, and the differences occur in the Cars vs. Environment interaction that follows.

Cars vs. Environment is a totally undefined interaction, the cars can run into a curb or a tree, or go over a cliff, or get hit by a train, or avoid getting hit by a train. The possibilities are endless, we can make some guesses as to what would typically happen, but it's really a guess. Better to indicate what the situation is post Car vs Car interaction (where we know the exact answer) and state that we don't know what the additional damage, if any, will be.

[The Niply Elder]

Originally Posted by Irishman

But the OP asked a basic physics 101 question that is answered with delta KE and conservation of momentum. Here is part of his post:

I'm not so sure. He proposed a scenario about colliding cars and finally asked which of two situations would "be more detrimental".

If the first test case was replaced with a red and green billiard balls, and the second case with a blue and yellow billiard ball, could you answer the question of "which one is more detrimental"? What would a postmortem forensic examination tell you? Nothing. There is nothing that you can conclude. Other than extreme simplifications of complex problems do not help you much.

[santorum]

Originally Posted by The Niply Elder

I'm not so sure. He proposed a scenario about colliding cars and finally asked which of two situations would "be more detrimental".

If the first test case was replaced with a red and green billiard balls, and the second case with a blue and yellow billiard ball, could you answer the question of "which one is more detrimental"? What would a postmortem forensic examination tell you? Nothing. There is nothing that you can conclude. Other than extreme simplifications of complex problems do not help you much.

I phrased the op rather poorly. About 20 years ago some kids in my rural hometown where playing chicken on the highway, and apparently they didn't set up ground rules and both 'chickened out' onto the same lane. I now accept that it's a frame of reference problem as most people here have mentioned (some with equations). I'll check out some of those crash test videos

[Irishman]

Originally Posted by The Niply Elder

If the first test case was replaced with a red and green billiard balls, and the second case with a blue and yellow billiard ball, could you answer the question of "which one is more detrimental"? What would a postmortem forensic examination tell you? Nothing. There is nothing that you can conclude. Other than extreme simplifications of complex problems do not help you much.

Billiard balls tend to have elastic collisions, so neither is very "detrimental". Unless you ramp the velocities up to 11, in which case the collisions stop being elastic. "Detriment" seems to require inelasticity.

It seems to me you're overparsing the word "detrimental". If you want to get into that level of detail, you're going to have to specify which make and model of car, and what angle they intersect, the orientation and position of each car, whether one car is empty and the other is loaded with exercise weights, etc, ad nauseum. There was nothing in the OP to suggest he wanted a run down of how much each car collapsed, or if the trunk was sturdier than the hood, or if the windshield cracked or not, etc. He asked a very generic question with limited constraints, suggesting that he was looking for the textbook situation.

Originally Posted by Cheesesteak

The other issue is that the summarized version glosses over the fact that the Car vs. Car interactions are identical, and the differences occur in the Cars vs. Environment interaction that follows.

Exactly, thank you for coming up with this phrasing.