Classic Vehicle Collision scenario

[adamrobarts]

Homework Statement

Im hopeless at interperating this, so ill just quote it:
"The masses of the vehicles involved in the collision have significant influence on injury occurence. Suppose a large car of 2000kg and a small car of 1000kg hit head-on when both are traveling at 60km/h. The mass ratio of the cars is 2:1. On collision, if the law of conservation of momentum is applied, the larger car will slow to 20km/h and the smaller car will be instantly propelled backwards at 20km/h. The larger car has a total velocity change of 40km/h while the smaller car has one of 80km/h. It is therefor not suprising that passengers in smaller cars have more severe crash injuries

Present an explanation as to why this factor is important in enhancing/reducing the risk of injury to occupants (Make specific references to physical principals involved)"

Hence its not an answer so much I am looking for, but an explanation.

Homework Equations

Since its talking about injury and damage to the car, i immediatly supposed it wanted reference to the Kinetic Energy formula (E=(mv^2)/2) and probably a reference to energy loss using the conservation of momentum theory.

The Attempt at a Solution

Initial Kinetic energy of the large car = 3,600,000J - the Initial Kinetic energy of the smaller car = 1,800,000J (No suprises there.)
Final Kinetic energies are: 800,000J and 200,000J for the larger and smaller cars respectivly.
The Kinetic energy lost in each case was: 2,800,000J and 1,600,000 for the large and smaller car respectively.
This was as far as i got moreorless; I concluded at this point that it must have sustained more damage because proportional to its mass, it was being subjected to a greater change of energy.

The forces applied to each other is equal, so i can't use that as a way to explain the hightened injury.
Interestingly i was expecting that the changes in energy would be the same - since the work applied to each other was also the same. Peculiar and unexplainable (unless I've missed something and made a mistake)


And that is about as far as I've come - I am probably just thinking in the wrong direction, looking for the wrong things; quite common problem of mine.
Any help would be appreciated.

Cheers, Adam.

 

[adamrobarts]

As an extra - I had from the beginning thought that if i were able to prove the loss of Kinetic energy was greater for the car (Or something like that) i could explain the aforementioned question. A quicky question perhaps: Now that i have found the losses of each vehicle, how am i able to precisely find how much was lost as heat+deforation etc and on which vehicles. For example - from this information i could say, "the smaller car lost 1,600,000J as deformation etc - which the larger one lost 2,800,000J as heat etc. Or i could switch it as vice versa. Is there really any clear way of knowing?

Sorry - but my mind is really hanging on this question - I am sure everyone knows what that feels like.

 

[adamrobarts]

- I've noticed that i am not getting responses; possibly because of the complexity of my explanation. Ill simplify it in one sentence.

<b> If a car1 has a head on collision with car2 (with car 2 being twice the mass of car1), and both were traveling at the same velocity, then why would the less massive car 1 sustain more damage and its occupants mroe severe injuries. </b>

This is my last question for the week - and i probably won't sleep until i get it >_<

If you need more detail just ask - If youre confused note it - If you can help, please do so

 

[mbrmbrg]

Just a thought--have you tried using impulse?

 

[adamrobarts]

I hadnt, but i just tryed...I think i can see the light.

Is my conclusion basically that the same force on a heavier car results in less damage and injury...Sorry if I am a tad thick, But staring at this question for such a long time now - i really want to understand it.

Thanks a lot mbrmbrg - you have really nailed it for me i think. Just to clarify though.

 

[mbrmbrg]

I hadnt, but i just tryed...I think i can see the light.

Is my conclusion basically that the same force on a heavier car results in less damage and injury...Sorry if I am a tad thick, But staring at this question for such a long time now - i really want to understand it.

Thanks a lot mbrmbrg - you have really nailed it for me i think. Just to clarify though.

I'd love to clarify it, but I can't really remember it so well, and at 1:45am my time, I will not let myself look it up. However, you are correct (as the problem tells you you will be ) in concluding that the heavier car will sustain less damage.

 

[adamrobarts]

I'd love to clarify it, but I can't really remember it so well, and at 1:45am my time, I will not let myself look it up. However, you are correct (as the problem tells you you will be ) in concluding that the heavier car will sustain less damage.

Thanks a lot mbrmbrg- i think youve saved my sanity. And yea - I am already sure that the larger car would sustain less damage ;) the only thing i have to do is explain it. But it seems fairly obvious now that I've considered the 'force' side of things.

Still, if anyone can assure me theyre welcome to ^_^

Thanks again . Peace.