Calculate Force of Car Wreck: A and B's Mass & Speed

[shutika]

Hi, I'm a person that likes physics a lot, but I'm unsure of how to address this problem I'm currently facing.

I was recently in a car wreck, and am backing myself up with evidence to go to court with. A woman hit me in the back right side of my car, and I'm not sure how to calculate the force of her car that was transferred to mine.

Okay. So I'll give you the givens, I suppose.

In this situation, I am A, the woman is B.

Okay, so the explanation is somewhat difficult.

The woman stopped at a stop sign, and then accelerated her car to go across an intersection, and into a parking lot. I was driving 25 mph through that parking lot, in a perpendicular direction to where she was going. The distance she traveled before she hit my car was about 50 feet.

My car spun a full 90 degrees. I'm not sure how to calculate the distance of that, my car is about 14 ft long though.

Her car weighs 1888kg, plus two 60 kg passengers. 2008 kg total.
My car weighs 1094kg, plus one 60 kg passenger. 1154 kg total.

I'm honestly not sure about how fast she was going when she hit me, but the frame damage suggests over 20 mph. Let's say 25 mph.

I'm a bit rusty on my physics, but wouldn't that be about 25100N of force, with an average acceleration of 18.3 fps?

If I'm wrong, please correct me.

 

[Cleonis]

I'm a bit rusty on my physics, but wouldn't that be about 25100N of force, with an average acceleration of 18.3 fps?

How much force is involved at any point in time is dependent on many details. The amount of force involved is not an informative piece of information.

For example:
If two marbles hit each other their time of contact is very very short, since marbles are very very hard. So in a marble-marble collision there will be an enormous spike in the contact force. In contrast with that: in today's cars the bodywork is designed to deform a lot on impact. The deformation elongates the time of contact. There is still the same amount of change of kinetic energy, but the impact is spread out over a longer interval of time, which gives a correspondingly lower maximum force.

The issue is: which details give useful information?
Amount of sustained damage is informative. Amount of displacement (spinning around) is informative. A guestimate of the maximum force is not informative.

Cleon

 

[sir-pinski]

First of all, I hope you are okay and that no one was seriously injured in the car accident. It's great that you are gathering evidence for the court case, and understanding the physics behind the impact can definitely strengthen your case.

To calculate the force of the car wreck, we can use the formula F=ma, where F is the force, m is the mass, and a is the acceleration. In this case, we have the mass of both cars and the acceleration can be calculated using the initial and final velocities and the distance traveled.

First, let's calculate the acceleration of the woman's car. We know that her car was traveling at 0 mph (stopped) and then reached a velocity of 25 mph in 50 feet, which is about 15.24 meters. Using the formula vf^2 = vi^2 + 2ad, we can calculate the acceleration to be 9.3 m/s^2.

Next, we can calculate the force of the impact using the mass and acceleration of the woman's car. F=ma, so the force would be (2008 kg)(9.3 m/s^2) = 18650.4 N.

To calculate the force on your car, we can use the same formula, but with the mass and acceleration of your car. F=ma, so the force would be (1154 kg)(9.3 m/s^2) = 10720.2 N.

However, this only gives us the force at the moment of impact. To calculate the total force of the car wreck, we need to consider the change in momentum. Momentum is calculated by multiplying mass and velocity, so we can calculate the momentum of the woman's car before and after the collision, and then subtract to find the change in momentum. This change in momentum is equal to the force of the impact.

Using the formula p=mv, the initial momentum of the woman's car would be (2008 kg)(0 m/s) = 0 kg*m/s, and the final momentum would be (2008 kg)(11.34 m/s) = 22767.2 kg*m/s. The change in momentum would be 22767.2 kg*m/s. This is equivalent to the force calculated earlier, 18650.4 N.

For your car, the initial momentum would be (1154 kg)(11.34 m/s) = 13090.36 kg*m/s