## Opposing forces

Hi - I got into a debate with a friend of mine today and was wondering if you could shed some light on this topic.

Two identical cars are moving at, say, 30 mph and hit head-on. There is some force and momentum involved there...

Would they hit with the same force and/or momentum as an identical car hitting a brick wall at 60 mph?

Assuming there is no elasticity between the cars, etc and they don't bounce off of the wall or other car....

 PhysOrg.com physics news on PhysOrg.com >> Iron-platinum alloys could be new-generation hard drives>> Lab sets a new record for creating heralded photons>> Breakthrough calls time on bootleg booze
 A good question! The answer is actually "no"! I know it seems counter-intuitive. Your instincts are telling you that because the relative speeds are the same, the impacts should be the same, but this isn't quite the case. What hurts you when you get in a car crash has to do with how quickly you accelerate to 0 mph. For simplicity's sake, we'll assume the wall is immovable, i.e. it's momentum doesn't change after the collision (which violates the conservation of momentum, but doesn't change the answer). The only thing that matters is the change in velocity during the collision (assuming both collisions take the same amount of time). If you hit another (identical) car head on, going at the same speed, the final velocities of both cars will be zero. If that same car is going that same speed, but hits a wall instead, the car's final velocity will also be zero. If both collisions take the same amount of time, and all three cars involved are going the at the same initial velocity, then the forces experienced by the drivers are identical. So, going back to your example, the driver of the 60 mph car would in fact feel twice the force that either driver of the 30 mph cars did. You don't have to take my word for it. If I remember correctly, the Mythbusters showed this.