I need a question Answered, Invovles Maths, Physics and cars.

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DavidB said:
So to sum up, crumple zones in a car are completely irrelevant? And here was me thinking they saved lives! Are you actually thinking that it takes no energy at all to bend masses of steel? :o
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But crumples zone are surely there to make the decelerations slower? Momentum still has to be conserved. Shouldn't effect how far the car gets pushed?

i'm not saying I'm right, i'm just curious.

edit: nvm should read posts better
 
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In the deformation process, no energy is converted to potential energy. What type of potential energy are you suggesting the kinetic energy is being converted into?
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Macroscopic kinetic energy (a car moving) can be converted into microscopic kinetic energy (temperature!). Remember that temperature is actually a macroscopic representation of a microscopic quantity (the kinetic energy of the molecules).

For a gas: http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution

What happens when an F1 car (or any car for that matter) brakes? You can probably see it if you watch F1, the brakes glow red hot. Primarily that is the kinetic energy of the car being transferred to heat (or microscopic kinetic energy).

Forget about the other car moving for a second: imagine if this girl had hit a 10ft thick super strong brick wall (well, don't imagine too hard, I wouldn't wish that on anyone!) at 30mph. If momentum was conserved at a macroscopic level, the car would bounce back at 30mph! I'm sure you've seen videos of crashes on TV into solid walls, they don't bounce back at 30mph. A significant amount of energy is dissipated through plastic deformation of the steel.

Duff-man, I'm off to start a PhD in Mechanical Engineering this year, what was your area?
 
E1mo said:
Duff-man, I'm off to start a PhD in Mechanical Engineering this year, what was your area?
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Numerical methods - specifically meshless RBF based methods for CFD and other PDEs. It's on the more theoretical side of what is covered by Mech Eng (big overlap with maths), but ME was the department that funded me so meh :p I only finished in January (doing a post-doc in a similar area now).

What about yourself? What will you be looking into?

I have to say, being a PhD student was great. Sure, you don't get as much cash as you would in industry, but it's hardly breadline when you take into account the lack of income tax and council tax. Also, you can work to your own timetable and have a lot of freedom about what you investigate. The most important thing is to have a good supervisor - even more so than the subject matter! I was lucky, and got a great guy for a supervisor.
 
DavidB said:
So to sum up, crumple zones in a car are completely irrelevant? And here was me thinking they saved lives! Are you actually thinking that it takes no energy at all to bend masses of steel? :o
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No... crumple zones just increase the time taken for the the acceleration to happen. People can go from 30mph to 0mph without any injury... it's only if the deceleration is too fast that it can injure people. Therefore, instead of slowing down in say 0.1 seconds, it takes 0.4 seconds, the rate of deceleration is much less, but is over a longer period of time. The total deceleration stays the same.

Obviously, energy is required to bend steel, but it is not used up. A bent piece of steel has no more energy than an unbent piece of steel. Otherwise if you bent a piece of steel then bent it back, you would have destroyed energy.

E1mo said:
Macroscopic kinetic energy (a car moving) can be converted into microscopic kinetic energy (temperature!). Remember that temperature is actually a macroscopic representation of a microscopic quantity (the kinetic energy of the molecules).

For a gas: http://en.wikipedia.org/wiki/Maxwell-Boltzmann_distribution

What happens when an F1 car (or any car for that matter) brakes? You can probably see it if you watch F1, the brakes glow red hot. Primarily that is the kinetic energy of the car being transferred to heat (or microscopic kinetic energy).

Forget about the other car moving for a second: imagine if this girl had hit a 10ft thick super strong brick wall (well, don't imagine too hard, I wouldn't wish that on anyone!) at 30mph. If momentum was conserved at a macroscopic level, the car would bounce back at 30mph! I'm sure you've seen videos of crashes on TV into solid walls, they don't bounce back at 30mph. A significant amount of energy is dissipated through plastic deformation of the steel.
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Ok ok ok so kinetic energy is transferred to heat but what about conservation of momentum?

If a car hits a brick wall, it accelerates the Earth in the direction the car was initially travelling, whilst the Earth accelerates the car in the opposite direction to the initial direction of the car.

Suggesting that the car bounces back at 30mph is a complete misunderstanding of conservation of momentum. I know you didn't say it did but you implied that it would if energy wasn't dissipated through plastic deformation of the steel.

Saying that momentum is conserved at a microscopic level is another misunderstanding. Conservation of momentum is different to conservation of energy.
 
Indeed, I'm going more for the theoretical side too, better than fighting over lab and technician time! At least you only have your own stupidity to blame when you can't get something done :D

I'll be looking into the Boundary Element Method for structural problems in plates and shells with specific application to the aerospace industry. Lots of maths :)

I've only met my supervisor once, but the meeting went well. The money works out pretty decently, I'm in London so I get a couple of grand extra, and it compares with a starting salary of 22k. Slim pickings for graduate jobs this year anyway, and frankly I'm not sure I would enjoy a lot of them.
 
E1mo said:
I'll be looking into the Boundary Element Method for structural problems in plates and shells with specific application to the aerospace industry. Lots of maths :)
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Boundary elements, nice :)

You might well know my supervisor then (not at first, but when you start researching). Prof. Henry Power. He did a lot of work in formulating the boundary element method, and he's an editor of the Engineering Analysis with Boundary Elements journal.

Have fun finding suitable solvers to handle the ill-conditioned matrices! :D
 
The point is, ordinaryjoe, that if the deceleration is affected by the structural deformation (as you now seem to have accepted), then so is the rate at which momentum is transferred back to the Earth (since this is proportional to speed and local coefficient of friction). As such, the distance travelled by the car (and the time taken to do so) are also affected by the deformation.

Given this, you can't quantify the initial momentum based only on the distance travelled by the combined body and the masses of the cars, even if we assume we know the coefficient of friction and that it is constant (which we don't and which it isn't). Since this is the only information we have, we cannot quantify the initial momentum without further knowledge of the effect that the deformation has on deceleration.
 
No no no no no no!!!!! Argh! The deceleration of the first car is affected by structural deformation! However, the second car (the one hit) will accelerate, gaining as much momentum as the first car loses. The total momentum of the 2 cars together when they first collide is equal to the momentum of the 2 cars when they collide. The momentum of the 2 together after that decreases uniformly, as the only force opposing motion (friction) is constant (not taking air resistance into account... it is an approximation).

As for the coefficient of friction, it is an approximation as well... It is not unreasonable to assume that the coefficient of friction is fairly constant seeing as the 2 surfaces are the same throughout.
 
ordinaryjoe said:
The deceleration of the first car is affected by structural deformation! However, the second car (the one hit) will accelerate, gaining as much momentum as the first car loses.
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This assumption is incorrect.

As the first car decelerates (while the structural deformation is taking place), it passes momentum *to the Earth*, as well as to the second car. You have no way of determining what proportion is transferred to the second car, without taking into account the specifics of the deformation.


Regarding the coefficient of friction, this can change dramatically as two interfacing materials go through different regimes. Think about it with regards traction control; traction control adjusts the relative speed between tyre and road in order to maximise the CoF. If the relative speed goes just a little too high, you get a dramatic change, and the CoF drops significantly. Anyway, even if you could consider the CoF as constant, you would need to know it's value in order to quantify the initial momentum (even under a rigid body assumption).
 
could we just not assume a rigid body, idealizes solution then subtract a nominal 15% form the calculated speed??

also other practical observations would help, did her airbag inflate (if she had one), this is only meant to happen over a set speed,

EDIT: we have also made a very basic assumption, which i think is untrue, how do we know the girl still dint have her foot down?
 
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Duff-Man said:
This assumption is incorrect.

As the first car decelerates (while the structural deformation is taking place), it passes momentum *to the Earth*, as well as to the second car. You have no way of determining what proportion is transferred to the second car, without taking into account the specifics of the deformation.


Regarding the coefficient of friction, this can change dramatically as two interfacing materials go through different regimes. Think about it with regards traction control; traction control adjusts the relative speed between tyre and road in order to maximise the CoF. If the relative speed goes just a little too high, you get a dramatic change, and the CoF drops significantly. Anyway, even if you could consider the CoF as constant, you would need to know it's value in order to quantify the initial momentum (even under a rigid body assumption).
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No... At of the momentum at the point of collision is either in the first or second car. None is passed onto the Earth except by friction (Please explain how you propose any is if you disagree), which can not be higher than the coefficient of friction x the reaction force of the Earth upon the vehicle. Which one are you suggesting increases?

About all the coefficient of friction changing stuff, when the car was braking, either the wheels were locked throughout or traction control was on throughout, so the deceleration would have been fairly constant (well with traction control, it would be alternating quickly enough to not have a noticeable effect on how far the car took to slow down compared to if it was a constant deceleration). Anyway, I stated clearly originally that I presumed the deceleration was 7m/s as this is what a previous poster suggested was feasible. What you are suggesting is that somehow, the momentum of the car gets transferred to the Earth, and to be honest, other than friction, there is no way the momentum could be transferred to the Earth. However, friction does not suddenly sky-rocket at the moment of impact, then go back to normal after.
 
ChrisJSY said:
Alright, I understand some people suffer from this.
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Whilst you may be "done" you have been consistently wrong. :)

Everybody is prone to these micro sleeps and it is not to be confused with Narcolepsy and condition where people fall asleep at any time without any warning.

A micro sleep is simply a few seconds of the brain shutting down because it simply is too tired to keep functioning but the conscious brain is forcing re-awake signals for example whilst driving. Had you been at home then the brain would have just entered sleep mode and you'd wake up at a latter time wonder why you are on the sofa and go to bed.

So there you are in a warm comfortable environment with a steady rocking motion (I.e driving) and before you know it you're asleep (even if it's for seconds). It's even easier to lapse at night as the flashing of lights operates on the brain in a way that enhances the sleepy feeling.

You don't have to have been awake for days or bone numbingly tired for this to happen. However all drivers should be aware of the warning signs and pull over, get some fresh air and maybe grab a coffee.
 
Thanks all.

The speed limit was 60kph BTW but i doubt many people stick too it. I know i dont most of the time.
I worded the same job(Ayear ago) as the girl and know how tired it makes you and how crap it is. Not blaming her in anyway.


I would ahve guessed she hi t at around 80kph, but then there are others that think it was much more
 
Jeebus. The scientists have got their notebook out :D

Great thread, just for the nerdy arguing alone :)

And ordinaryjoe - the coefficient dynamic constant rule when run through several simulations taking x to equal the inverse of y (when z = z^z) clearly shows you are wrong to within -5/+15%.
 
ordinaryjoe said:
No... crumple zones just increase the time taken for the the acceleration to happen. People can go from 30mph to 0mph without any injury... it's only if the deceleration is too fast that it can injure people. Therefore, instead of slowing down in say 0.1 seconds, it takes 0.4 seconds, the rate of deceleration is much less, but is over a longer period of time. The total deceleration stays the same.

Obviously, energy is required to bend steel, but it is not used up. A bent piece of steel has no more energy than an unbent piece of steel. Otherwise if you bent a piece of steel then bent it back, you would have destroyed energy.



Ok ok ok so kinetic energy is transferred to heat but what about conservation of momentum?

If a car hits a brick wall, it accelerates the Earth in the direction the car was initially travelling, whilst the Earth accelerates the car in the opposite direction to the initial direction of the car.

Suggesting that the car bounces back at 30mph is a complete misunderstanding of conservation of momentum. I know you didn't say it did but you implied that it would if energy wasn't dissipated through plastic deformation of the steel.

Saying that momentum is conserved at a microscopic level is another misunderstanding. Conservation of momentum is different to conservation of energy.
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I think you are underestimating the energy that it takes to bend the metal, however for arguments sake we could just say that the collision absorbs between 20-40% of the impact energy.

As such the solution to the problem is straightforward, however the assumptions you make introduce large errors in the reult.

In reality, if we knew the CoF accurately and the energy absorption ability of the crumple zones, we could easily solve the problem based on 3 formulae:

F=MA
W=FS
Ke=1/2MV^2
 
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