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

M0T · 3 Apr 2009 at 12:16

ChrisJSY said:
EDIT: Nobody I know have this problem of not having a choice and falling asleep when extremly tired.
I've have this conversation before so I know this with them at least.

If you have a medical condition, then what the hell are you doing driving whilst tired when you know you don't have a choice staying concious .

I might sound ridiculous, but I don't have any kind words for what you sound like.

Like I said, if you have problems falling asleep whilst in command of a 1000kg + vehicle driving at speeds in excess of a human running, you have to be VERY SPECIAL in the head.

PS. Had to edit this so many times to make any sort of sense.

I used to work with a guy who fell asleep when he was at the wheel of a car. He was 22 and had no medical conditions but had been made to work for 3 days straight with maybe 2 hours off between shifts. On the third night he went back to his hotel to get changed and fell asleep whilst driving down the road, his car flew off the road into a tree and he ended up in a 9 month coma (got some brain damage too).

It gets to a point where you can fall asleep without even realising it because you are that tired (micro sleep I think it is called).

Duff-Man · 3 Apr 2009 at 12:19

M0T said:
It gets to a point where you can fall asleep without even realising it because you are that tired (micro sleep I think it is called).

I agree, but if you choose to put yourself in control of a vehicle in such a state, then you should be responsible for any damage caused by falling asleep at the wheel.

Your friend could have taken a taxi, or a bus, or other transport which wouldn't have required his constant concentration. Not trying to sat he deserved what he got or anything, just pointing out that we must take a degree of responsibility for our state of mind whenever we control a dagerous piece of machinery (including a car).

Col_M · 3 Apr 2009 at 12:24

Biohazard said:
Hard to work out how much energy would be absorbed by the impact..

Exactly.

Any sort of calculation would use a lot of vague assumptions. The police accident investigators may have a way of getting a good approximation by using data from previous accidents.

ChrisJSY · 3 Apr 2009 at 12:35

M0T said:
It gets to a point where you can fall asleep without even realising it because you are that tired (micro sleep I think it is called).

Alright, I understand some people suffer from this.
I don't, in fact it takes me at least an hour to get to sleep no matter what, not fun!

Edit: Deleted rest.

I'm done

ordinaryjoe · 3 Apr 2009 at 13:13

Crumple zones will have no effect on the distance which the 2 cars travel after the crash.

say the cars decelerated at 7m/s^2 and the distance was 20m.
0=x^2-7x20 x^2=140 x=about 12m^s (speed when the 2 cars collided)
1285kg Celica travelling at y m/s has energy 640 y^2
Together the cars have mass 1820kg and have energy 640 y^2 which equals 910x12^2=131 000=640 y^2
y^2 = 204
y= 14m/s = 31mph

Duff-Man · 3 Apr 2009 at 13:34

ordinaryjoe said:
Crumple zones will have no effect on the distance which the 2 cars travel after the crash.

say the cars decelerated at 7m/s^2 and the distance was 20m.
0=x^2-7x20 x^2=140 x=about 12m^s (speed when the 2 cars collided)
1285kg Celica travelling at y m/s has energy 640 y^2
Together the cars have mass 1820kg and have energy 640 y^2 which equals 910x12^2=131 000=640 y^2
y^2 = 204
y= 14m/s = 31mph

You have not taken into account the energy required to deform the metal on either car. This energy will be significant, and is the reason that modern cars are designed with "crumple zones" and other energy absorbing features.

Basically, you are trying to apply particle / solid body mechanics to a scenario where they are not applicable.

ordinaryjoe · 3 Apr 2009 at 13:41

No but conservation of momentum - in deforming the metal, it is also accelerating the car. The only force opposing the motion is friction between the car tyres and the road (and a bit of air resistance which is comparatively negligible)

Duff-Man · 3 Apr 2009 at 13:48

ordinaryjoe said:
No but conservation of momentum - in deforming the metal, it is also accelerating the car. The only force opposing the motion is friction between the car tyres and the road (and a bit of air resistance which is comparatively negligible)

You need to consider both conservation of momentum AND conservation of energy to solve a generalised two-body interaction.

The transfer of momentum to the earth is proportional to the speed at which the car is moving, and the coefficient of friction (which itself will be a dynamic variable). The speed and acceleration of the car will change with time during the collision (due to the specifics of the deformation energy), leading to a highly nonlinear problem whereby the nonlinearity is a function of the material properties of the two cars and the specifics of the collision.

Not everything can be modelled assuming a particle assumption, a one-dimensional linear ODE, and neglecting internal inertia. Life would be a hell of a lot simpler if it did, and there would be very little need for engineers.

I'm guessing you're doing A-level maths or physics? If so you'll come across nonlinear problems when you get to Uni.

ordinaryjoe · 3 Apr 2009 at 13:50

No but conservation of momentum exists. Where do you think the momentum went when the cars crashed? Sure, energy was used to crumple the crumple zones, but the energy does not stay there... the crumple zones have no more energy when they are crumpled as before. All the crumple zones do is increase the time taken for the momentum (kinetic energy) to be transferred - they don't destroy momentum or energy. Momentum can not disappear.

Duff-Man · 3 Apr 2009 at 13:53

ordinaryjoe said:
No but conservation of momentum exists. Where do you think the momentum went when the cars crashed? Sure, energy was used to crumple the crumple zones, but the energy does not stay there... the crumple zones have no more energy when they are crumpled as before. All the crumple zones do is increase the time taken for the momentum (kinetic energy) to be transferred - they don't destroy momentum or energy. Momentum can not disappear.

I think you're getting a bit confused here.

Momentum is transferred to the earth via friction.

Energy is transformed from kinetic to potential via the deformation process, and is also transferred to the earth via deceleration.

The two interact, leading to a non-linear deceleration.

Think about it...

E1mo · 3 Apr 2009 at 13:59

No but conservation of momentum - in deforming the metal, it is also accelerating the car.

Your wrong, plastic deformation of the metal will convert kinetic energy in the collision into heat. The plastic deformation is a thermodynamically non-reversible process, the momentum doesn't somehow go back in to accelerating the car.

Of course, you can say that it is insignificant, but the effect is there. You need to show it is insignificant before you can discount it. I suspect it isn't an insignificant effect.

I think this graphic should persuade you the complexities of car collisions:

http://en.wikipedia.org/wiki/File:POLO1a.JPG

ordinaryjoe · 3 Apr 2009 at 14:00

Momentum is transferred to the earth via friction from the brakes. The crumple zones have nothing to do with this and the brakes only have an effect once the cars have collided.

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?

No energy is transferred to the earth via deceleration except that done by friction. The car is going horizontally, so the only force towards the Earth is mavity. Any more would mean there would have to be an equal opposite force pushing something up.

Think about it

Duff-Man · 3 Apr 2009 at 14:06

ordinaryjoe said:
No energy is transferred to the earth via deceleration except that done by friction. The car is going horizontally, so the only force towards the Earth is mavity. Any more would mean there would have to be an equal opposite force pushing something up.

You've contradicted yourself here. You say that the only force towards the Earth is mavity, and yet you also state that there is a deceleration due to friction. F=m.a remember? The frictional force is acting on the Earth, in the direction parallel to its rotation.

E1mo has already answered your question about deformation energy.

You'll understand more about the complexities of such interactions when you go further with your studies, so don't worry about it too much.

By the way, I have a PhD in mechanical engineering, so I do actually know what I'm talking about

I can't spend more time explaining this further though (I have a job to do!), so if you want to learn more I suggest you take a look either at an engineering textbook, or google for collision dynamics.

ordinaryjoe · 3 Apr 2009 at 14:16

I meant towards as in in the direction of the earth - not acting upon the earth. Yes... I know F=mA but how is this relevant?

Friction = coefficient of friction x reaction force (force of the Earth upon the car). The reaction force is constant throughout the collision, as is the coefficient of friction. There are no other forces opposing the horizontal motion, so the deceleration is constant.

What does deformation energy mean? It is not a type of energy at all but rather a phrase used to describe the amount of energy needed to deform something. This does not answer the fact that momentum can not disappear. Please explain where you think the horizontal momentum goes!

Duff-Man · 3 Apr 2009 at 14:31

ordinaryjoe said:
Please explain where you think the horizontal momentum goes!

To the Earth. It adjusts its rate of rotation (albeit by an immesurably small amount, due to the relative masses).

Okay, forget about cars for a minute. Consider yourself going for a run. At t=0 you're standing still; you [as an isolated system] have no momentum. You then start running; you now have a non-zero momentum [again, considered as an isolated system]. When you stop, you once again have no momentum. Where has the momentum gone, and where did it come from in the first place?

The answer, of course, is that it is transferred to the Earth. Taking the larger system of you AND the Earth the total momentum does not change, but considering yourself as an isolated system, you have an apparent source of momentum. The force that gives rise to this (apparent) change of momentum is the friction between your shoes and the earth, which acts parallel to your direction of motion. An equal and opposite force is applied to the Earth.

ordinaryjoe · 3 Apr 2009 at 14:34

Yes I understand this, but friction has a maximum value. That value does not change unless if the coefficient of friction changes, or the reaction force of the Earth upon the car (or runner or whatever) changes. Neither of these change in the original question, so therefore, the force of friction is constant whenever the car is not still. Therefore, as momentum is conserved, and the momentum given to the Earth is equal to the friction, there is no other force to consider.

Duff-Man · 3 Apr 2009 at 14:42

ordinaryjoe said:
Yes I understand this, but friction has a maximum value. That value does not change unless if the coefficient of friction changes, or the reaction force of the Earth upon the car (or runner or whatever) changes. Neither of these change in the original question, so therefore, the force of friction is constant whenever the car is not still. Therefore, as momentum is conserved, and the momentum given to the Earth is equal to the friction, there is no other force to consider.

You seem to be arguing for arguments sake, now. Friction has a "maximum value?" What does that even mean? :confused:

Also, why do you think that the coefficient of friction would not change? Just because it is given as constant in A-level mechanics questions (in order to produce a linear ODE which can be solved analytically) does not mean this is the case in the real world. In fact, it will be a material-dependent property which will change with time, and locally with space (depending on the nature of the local interaction between car and surface).

I really can't spend any more time on this... If you must convince yourself that particle dynamics are somehow applicable to all situations, then feel free. You won't get very far though.

ordinaryjoe · 3 Apr 2009 at 14:49

What the heck? I'm arguing for argument sake? No I'm not. Friction can not be higher than the coefficient of friction (which is constant between 2 given surface) multiplied by the reaction force, but it can be lower, but only when the surfaces are still in relation to each other. Therefore, friction is at it's maximum possible value. This is what I mean. Why would it change? It does not to any reasonable degree at all... maybe the tyres getting hot would slightly change it but that is all. The deceleration is constant as the force of friction is constant upon a constant mass. Stop being so patronising. Particle dynamics are not perfect but they are perfectly suffice for this situation and have given a perfectly reasonable answer... much more useful than just saying "I don't know" then criticising people who try to help

muon · 3 Apr 2009 at 14:58

If I could remember any of my A-level mechanics modules I could probably do this.

Oh well, I'm sure there are physicists/engineers here who can give a detailed answer.

DavidB · 3 Apr 2009 at 15:14

ordinaryjoe said:
What the heck? I'm arguing for argument sake? No I'm not. Friction can not be higher than the coefficient of friction (which is constant between 2 given surface) multiplied by the reaction force, but it can be lower, but only when the surfaces are still in relation to each other. Therefore, friction is at it's maximum possible value. This is what I mean. Why would it change? It does not to any reasonable degree at all... maybe the tyres getting hot would slightly change it but that is all. The deceleration is constant as the force of friction is constant upon a constant mass. Stop being so patronising. Particle dynamics are not perfect but they are perfectly suffice for this situation and have given a perfectly reasonable answer... much more useful than just saying "I don't know" then criticising people who try to help

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?