Crash simulation on Mythbusters [duplicate]

Question

I remember an episode of mythbusters where they were busting myths to do with a head on collision between two cars.

They said that instead of crashing two cars into each other at 50mph they would crash a car into a stationary object at 100mph because the energy involved in the crash would be the same.

Later on they corrected themselves to say that the energy is not the same. But I can't figure out why this would be the case?

Can someone explain if these two scenarios are the same or not. And why?

Answer 1

The Mythbusters hosts realized that the important issue in a head-on collision is what is happening inside your vehicle. There is indeed twice the kinetic energy involved with one car colliding with an immovable object at 80 mph vs. two cars colliding head-on at 40 mph. However, Newton's third law requires the immovable barrier to provide an equal and opposite force when it stops a car that collides with it. This means that from the standpoint of an individual driver, there is no difference between two cars colliding head-on at 40 mph, and a single car colliding with an immovable barrier at 40 mph. In principle, you and your car experience the same stopping force in both instances.

Answer 2

In first case: Total Energy $$E_1= \frac{1}{2}mv^2 + \frac{1}{2}mv^2=mv^2$$ In second case: Total Energy $$E_2=\frac{1}{2}m(2v)^2=2mv^2$$ Thus, total energy doubles i.e $$E_2=2E_1$$

Answer 3

Imagine a thought experiment in which the two cars and their contents are identical mirror images of each other.

In this perfectly symmetrical universe, after a 50 mph crash, the cars break up symmetrically: because the cars and contents are identical in every way, every fragment is emitted at exactly the same time from the same position and at the same speed, except for reflection.

Not only does every particle of one car collides with its corresponding particle from the other car, every collision happens in the plane of symmetry, with each pair of particles either stopping dead or bouncing away from each other.

But this is identical to the result of one car crashing at 50 mph into an immovable infinitely large wall where the plane of symmetry was.

Therefore, two identical cars at 50 mph each crashing is, in principle, the same as one car crashing into a wall at 50 mph — and different from a car crashing into the wall at 100 mph!