# Car Accident Reconstruction

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1. Jan 18, 2010

### Krazykaveman

My physics professor gave us a lab in which we have to do accident reconstruction. The difficulty I am having is that we have not gone over how to calculate collision with coefficients of restitution in class. So far we've only done completely elastic or inelastic, yet now he expects us to do this on our own.

1. The problem statement, all variables and given/known data
Car 1 traveling east and claims they were going 15 mph.
Car 2 is traveling north and claims they were going 40 mph.

After collision, Car 1 skids 66.8ft, 30º north of east
Car 2 skids 16.7ft, 9º south of east.

The coefficient of friction is .8 and the coefficient of restitution is approx 41%.

Car 1 claims that Car 2 rammed into the side of her car.
Car 2 claims that Car 1 rammed into the side of her car (travelling at a high rate of speed)
Car 2 had the right of way.

2. Relevant equations
1/2mv^2 = μmgd (1)
KE(init)/KE(final) = C.O.R. ^ 2 (2)

3. The attempt at a solution
Using the distances traveled and the amount of friction involved, I calculated the speed of each car the moment after collision. Now I am trying to verify the initial speeds of each driver. I know one of the drivers were speeding by using eqn. 2 and finding the velocities in the center of mass frame of reference, however this method will not help me guess what the initial velocities would be but just that the initial speeds are too low. I currently suspect that car 1 was going at a much higher rate of speed and was hit by car 2.

How would I use this data and use equations for coefficient of restitution to figure out what the initial velocities of the cars would be if one were speeding?

2. Jan 18, 2010

### ideasrule

Write out both the conservation of momentum equations and the conservation of energy equation. The final total kinetic energy is equal to the coefficient of restitution times the initial total kinetic energy. There's nothing mysterious about this; it's just how the coefficient of restitution is defined.

3. Jan 18, 2010

### Krazykaveman

So just to clarify, is the following expression true?

$$1/2m_1v_1_f^2 + 1/2m_2v_2_f^2 = (1/2m_1v_1_i^2 + 1/2m_2v_2_i^2) * C.O.R.$$

And the velocities are not relative to the center of mass or anything like that?

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