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# CAR COLLISION

Hi:
A physics question: I was in a car collision recently and the other party alleges that the impact was such as to push his car 3 metres sideways (ie at 90 degrees to wheels). Assuming that both cars weighed a tonne and he was stationery (actually turning across me very slowly) then is it possible to calculate the speed I was doing at impact? I think it was below 20mph but the suggestion is that I was speeding. I know f=ma but newton gets involved and I am lost!
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Richard Teasdale
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3 Solutions

Commented:
To know that, you would need to know the coefficient of static friction and kinetic friction between his wheels and the road. If there is enough force to move the vehicle at all, then you will have overcome the static friction and be dealing with kinetic.

According to this
http://www.engineeringtoolbox.com/friction-coefficients-d_778.html
Kinetic friction between rubber and dry asphalt is between .5 to .8
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Commented:
This is probably the relevant calculation.
http://forensicdynamics.com/stopping-distance-calculator
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Commented:
Ah, that saves me from the physics work I was trying to do on my scratch pad.
Looks like you 20 mph sounds a little high even.
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Commented:
You'd have to adjust it assuming that only one car was skidding, and only one car was initially moving, but those effects tend to oppose each other, so it's probably a reasonable rough approximation given other unknowns.
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Commented:
The calculation from the link will give you the estimated initial speed of the car you hit. The loss of energy from the cars compressing at impact will take some of the force away so your car would have been moving a little faster than the calculation, but assuming the cars didn't compress much, it should be close.
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Software DeveloperCommented:
http://en.wikipedia.org/wiki/Impulse_%28physics%29

but as ozo said, the results will be vague ;-)
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Financial ControllerAuthor Commented:
What a great response! Thanks you very much for pointing me in the right direction!
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Commented:
A perfect collision between equal mass cars would transfer all the speed to the originally stationary car, leaving yours stationary.
Which would make calculation at the above link perfectly appropriate.
More likely, both cars were moving after the collision.
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Software DeveloperCommented:
You're welcome ;-)
And if the points had not been distributed that even, I would have said, that you should have accepted ozo's solution ;-)
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Financial ControllerAuthor Commented:
Maybe so but I think all three of you have contributed with thought and courtesy. So you all get the points  in my eyes.
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Software DeveloperCommented:
That's what I wanted to say ;-)
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Commented:
More likely, both cars were moving after the collision.

Yes. So the initial speed calculated from the link would really be something like half the original speed of the first car.

So to move an identically weighed car 3 meters with minimal compression, the first car would have been going about 28 mph?
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Commented:
Can't give you a definitive answer, but consider this. If you were on ice, a little push could move the car quite a distance. So the important variable in this calculation is how much friction or resistance was the ground providing? If we assume that the street was dry and the wheels were exactly 90 degrees from the direction of motion, his wheels would be providing the maximum resistance to motion. That would be like having you brakes locking up your wheels. If you were traveling at 20mph and locked up your brakes, would you be able to stop within 3m? Probably not. So transferring that force (momentum) from you vehicle to his would set his vehicle in motion. (Like those Newton balls that hang from strings.) His car would then need to stop by the resistance provided by his locked up wheels. Even if only half of the force is transferred (due to similar mass of the vehicles) then it is still possible to move 3m after the impact.

I suspect that the real issue here is that the other guy was in the wrong for turning in front of you and he is just trying to deflect the blame with any excuse he can think of. You may have an easier route proving that you had the right of way and he was totally wrong. If he had the right of way, you're going to have a hard time with this case.
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Financial ControllerAuthor Commented:
Thanks for that MarvinM80 - but the case was lost. THe other side did turn in front of me but argued that I went through a bus stop (!) so he did not see me until too late. THe bus stop was some 50 metres from the impact and I was doing about 20mph when I hit him so I was trying to work out what speed  I could possibly be doing  through a bus stop, with a queue of stationary traffic in the actual road, at 5.45pm on a wet november night! Lewis Hamilton I am not!
It was ludicrous but my side folded.
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Commented:
Too bad about the case. It was an interesting exercise in physics though. I don't know how many factors it would require to accurately calculate your speed, but your 20mph estimate sounds completely reasonable. Thanks.
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