# Classic Vehicle Collision scenario

1. May 12, 2007

1. The problem statement, all variables and given/known data
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 travelling 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 im looking for, but an explanation.
2. Relevant 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.

3. 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 eachother is equal, so i cant 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 eachother was also the same. Peculiar and unexplainable (unless ive missed something and made a mistake)

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

2. May 12, 2007

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 - im sure everyone knows what that feels like.

3. May 13, 2007

- Ive 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 travelling 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 wont sleep until i get it >_<

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

4. May 13, 2007

### mbrmbrg

Just a thought--have you tried using impulse?

5. May 13, 2007

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 im a tad thick, But staring at this question for such a long time now - i really want to understand it.

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

6. May 13, 2007

### mbrmbrg

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.

7. May 13, 2007