I’ve always loved Mythbusters and I’m usually happy with the way they do things.
One time, though, I think they got it wrong. The episode that I’m on about aired nearly a year ago, and I made a mental note to point out the inaccuracy. The myth was the revisited version of the one about fusing a hatchback between two big lorries in a crash, called “Compact Compact Supersized”. The idea being that the two lorries crashing head-on would have enough energy to completely squash the little car.
Because it’s so long ago, I don’t remember the specifics, but it went something like this:
“The myths says that there are two trucks which crash head-on, each going 50 mph. Because it’s hard to precisely co-ordinate two trucks, instead we’re going to have just one truck going 100 mph into a brick wall with a hatchback in front.”
This is where I think there’s a problem. The energy – which is what would cause damage to the car – in the two scenarios is not the same.
Energy of a moving object (called kinetic energy), such as the energy of each lorry, is calculated as such:
Ek = ½mv2
So in the original scenario with two trucks, the total kinetic energy is:
2 × ½mv2 = mv2 (where v = 50)
In the second scenario, there is only one truck carrying all the energy, but its velocity is doubled. Therefore the kinetic energy is:
½m(2v)2 = ½m4v2 = 2mv2
This clearly shows that the energy involved in the replacement scenario with just one truck going double the speed is twice that of the original myth scenario.
It doesn’t affect the outcome of the myth, thankfully, but it’s still quite a big mistake to overlook.
UPDATE: How fast should the single car been going?
It should have been going the square root of two (about 1.4) times as fast as in the original scenario, which would make it about 71 mph.
Here’s the maths:
½m(root 2 * v)2 = ½m2v2 = mv2 ((root 2)2 = 2 by definition)
This is the same as the energy as in the original scenario.