Collision- Am I thinking about this the right way?

[Oldblood]

Homework Statement

Whats more destructive? A front collision between 2 identical cars, or 1 car with the same speed but driving into a mountainwall?

Homework Equations

Equations for conservation of energy and momentum.

The Attempt at a Solution

Hi guys, I am just wondering if I am thinking about this the right way or if there are any errors in my reasoning? For the front collision. The 2 cars will have a kinetic energy of 0.5mv^2 each. Let's assume the collision is totally Inelastic. Thus no kinetic energy is left. Due to symmetry the kinetic energy is transformed equally into both cars deforming them equally. So the total energy that had a destructive act on 1 car is 0.5mv^2. Now to the other case. I am going to think about this as a collision between a very large and very small object, where the large object is at rest. So the total energy now is 0.5mv^2. Since we now have 2 different masses, where they both are not at rest, we have a net momentum. So assuming the car totally stops it must transfer some of its kinetic energy to the large object, because if not the total momentum would be 0 and then it wouldn't be conserved since we had a net momentum before the collision. This means that the whole package of 0.5mv^2 does not go all the way to deformation, but some of it must go to transfer kinetic energy to the larger object, thus the impact is less destructive. This isn't really my homework, it was just a discussion I had with a friend.

Conclusion: You would rather hit a mountain wall then a front collision with the same speed (regarding damage on the car and in an ideal situation like this)

 

[gneill]

Heh. When you're dealing with such enormous differences in masses (Car versus the Earth! now in theaters!) one often finds oneself dealing with near infinities or near neglibililities and falling into false assumptions about them.

In such cases it's often instructive to make a change of reference frame to get rid of the seeming paradoxes. Here you can switch to a center of momentum frame. In this frame, the mountain (attached to the whole Earth) and the car have equal and opposite momenta, so that the total momentum for the system is zero both before and after the collision. Problem solved.

With the great mass discrepancy between the car and the Earth, you'll find that the center of momentum frame looks an awful lot like the original frame of reference...the details being a good many decimal places down and to the right.

 

[arjunaphysik]

I saw this on MythBusters.

Assuming a totally inelastic collision, there is equal energy transfer between both cars. Similarly because of the disparity in mass of the mountain and the car, whatever pitiful amount of kinetic energy is transferred by the car into the mountain, the mountain remains unmoved (absorbing all of the energy).

So, the answer to "which collision is more destructive" really boils down to this:

Which would you rather have in your face: rocks (from the mountain), or glass (from the other car's windshield)?