Speed and distance in a car crash

[elijahfischer]

I had a car accident and need to go to court to prove my case. Please help me figure this out with what formulas I need to use. Also please explain details so I can explain it to the judge. Thanks. Here it is: I was traveling when I hit a car that pulled out in front of me. She claims she was making a left turn and that I hit her vehicle on the corner hard enough to push her vehicle sideways. I need to know how fast I would need to be going to move the back of her vehicle sideways anything more than an 1".
Here is the data:
Weight of my vehicle: 3196 lbs
Weight of her vehicle: 3009 lbs
My speed before impact: 25 MPH
Her speed before impact: o mph
Payment: Asphalt
Weather conditions: Dry 70 degree F

 

[Simon Bridge]

Jones and Childers report coefficients of friction of about µ=0.7 for dry roads

The force opposing motion would be µW=(M+W)a: W is the weight of her car and M is the weight of yours - a is the deceleration. the distance slid is given by d=v²/2a where v is the initial speed of both cars.

Back of envelope, you'd use conservation of momentum to estimate the speed of both vehicles together after the collision but before lateral movement.

Mu=(M+W)v where u is the speed of your car before the impact.

Plugging in the numbers I get 27cm lateral movement: about a foot.
There's an awful lot of assumptions in that but at least it does not look all that sensitive to even quite large changes in speed (I still get less than a foot for u=50mph).
That's for pushing the whole car - for just the back you'd be rotating about the front wheels and only the weight on the back wheels will count for F. If I guess half (it will be less - engine is in the front right?) and just stay linear the guess turns into 72cm - a bit over two feet.

However: my experience is that judges are seldom impressed by this sort of reasoning unless you get an expert witness to deliver it. What you really need is an expert in accidents or a practical experiment.

 

[256bits]

If she attempted a left turn from opposing traffic or from a side street while it was not safe to do so would mean that her manoeuvre was the probable cause of the accident.
If you rear-ended her then most likely your inattention on the road that is the probable cause of the accident. Unless she changed lanes and braked in front of you and you hit her in which case the main party at fault is for a debate.
Unless you can prove to the judge that you are an expert in some aspect of road collisions and damage ensued, I doubt that a momentum and energy calculation would impress the judge, as SB stated.

 

[elijahfischer]

Thanks for the help. Will keep that in mind about want impresses the judges.

 

[PJC01]

First, it is important to establish the fundamental principles of physics that apply to this scenario. When a moving object collides with another object, the force of the impact depends on the mass and velocity of the moving object. This force can cause the other object to move, change direction, or even deform.

In this case, we have two objects (the two vehicles) with known masses and speeds before the collision. To determine the force of the impact, we can use the formula F=ma, where F is the force, m is the mass, and a is the acceleration.

In order to move the back of the other vehicle sideways by more than an inch, there must be a significant amount of force applied. We can calculate the minimum force required using the formula above, and then work backwards to determine the minimum speed needed for this force to be produced.

To calculate the force, we need to know the mass of the other vehicle and the acceleration it experienced. We can determine the acceleration by dividing the distance (in this case, 1 inch) by the time it took for the vehicle to move that distance. This time can be estimated based on the average reaction time of a driver, which is around 0.75 seconds. So, the acceleration would be 1 inch/0.75 seconds = 1.33 inches per second squared.

Now, we can plug in the values into the formula F=ma. The mass of the other vehicle is 3009 lbs, which would be converted to 1366.75 kg. The acceleration is 1.33 inches per second squared, which would be converted to 0.033782 meters per second squared. So, the minimum force required would be F= 1366.75 kg x 0.033782 m/s^2 = 46.18 Newtons.

Next, we can use the formula F=ma again to determine the minimum speed needed for this force to be produced. We know the mass of the other vehicle (1366.75 kg) and the acceleration (0.033782 m/s^2), so we can rearrange the formula to solve for velocity (v). This gives us v= F/m = 46.18 N / 1366.75 kg = 0.033782 m/s.

Finally, we need to convert this speed from meters per second to miles per hour (mph). To do this, we can use the conversion factor 1