Edit: Assume both cars are identical
In: 0
It’s basically the same.
The momentum is the same, the crash forces will be the same.
The only difference is using a different frame of reference, so you’ll end up with some terms cancelling out in the force and momentum equations.
**Momentum:**
1.) p=mv –> mv initial = mv final
2.) m-car1 * v-car1 + m-car2 * v-car2 = m-final * v-final
3.) m-car1 * v-car1 + m-car2 * v-car2 = (2 * m-carN) * v-final (assuming the car masses combine)
let’s say the masses are the same and just divide by 1 car’s mass (this will work with different masses, though the change in speed will be smaller for the more massive vehicle – both scenarios will be identical.)
4.) v-car1 + v-car2 = 2 * v-final
So here we have the difference, you can do 100 + 0 or 50 + (-50). Either way, the cars will be going half the final differential speed relative to their initial speed.
You can also shift the frame of reference:
to car1: 0+(-100) vs 0 + 50 + (-50) [going car ground car for the 2nd case here]
to car2: 100 + 0 vs 50 + (-50) + 0
Note they all add up to the difference in speeds. So car 1 is going from 100 to 50, or 50 to 0 (-50mph), and car 2 is going from 0 to -50, or 50 to 0 (-50mph)
**Energy:**
Then you move energy imparted – which is based on the change in velocity. Both cars see a delta of 50mph in each scenario, so will see equal damage.
**Force:**
To get the peak forces imparted on the passengers, you need to know about the crumple zones. Car crash rails are designed to [crush with a constant force](https://www.youtube.com/watch?v=TM5dyY8zfxs), but I think you see an increase in force as you get further into the vehicle. (Imagine crushing a pyramid, you will get into more material the further you go)
To calculate forces, I would look at the energy imparted, then see how much distance that gets you into the crumple zone, then back out how much force that would impart.
**Real world:**
There is one difference here, you have the “ridedown” – in one scenario, post impact, the cars are at 0mph relative to the ground, in the other they are both going 50mph. After a crash like this, the cars won’t have the wheels and brakes all attached/in good shape. (Even if they were, I don’t think either driver would be able to apply sensible control) At 50mph they’d be able to roll along for about a mile or steer into something and hit it.
So if I had to choose a scenario, I would rather be in the +50 -50mph crash.
Here’s a more detailed breakdown of the math: https://www.youtube.com/watch?v=JyCVl95UDxw
Latest Answers