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The car vs. car paradox


bobbyburns

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You have two cars.

They're travelling right at each other on a collision course; each one is going at precisely 50mph.

They hit each other...as you could assume.

mythbusters_cars.jpg

Does that equate to one car hitting a wall at 100mph? Or is it something different?

I became interested in this paradox after watching Mythbusters' rendition of it (which is, of course, the best show in our current universe).

Their take on it was conducted through a full scale test. Their findings showed that the collision was identical to ONE car hitting a concrete wall.

The momentum equations behind this make sense, too. The car on the left (let's say they both have a mass of 10kg and are travelling at 20m/s) has a momentum of (10kg)(20m/s)=200kg*m/s. Equally, the car on the right has the same momentum.

So, the car on the left's momentum is negated by the car on the right.

That's the "real world" test result.

Any other arguments may hold validity...but I strongly reject your reality and substitute my own.

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So the momentum is the same, but the kinetic energy of the two-car system moving towards each other at 20 m/s each is (2cars)[(1/2)(10kg)(20m/s)^2]=4000J.  The kinetic energy of one car moving twice the speed into a wall is (1car)[(1/2)(10kg)(40m/s)^2]=8000J.  Why do the collisions look the same if one needs to dissipate twice the energy of the other?  Shouldn't the single car collision look four times worse than the two car collision (one car dissipating 8000J=8000J/car but two cars dissipating 4000J=2000J/car.  If one dissipates four times the energy per car of the other, why do they look the same)?

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