The other day I saw this video from the Mythbusters and was disappointed that they made a mistake. Can you spot it?
For those who didn’t watch the video, the summary is that they wanted to know if two cars crashing into each other at 50 miles per hour was the equivalent to a car crashing into a brick wall at 100 miles per hour. Initially Jamie said yes, but fans said no, so they tested it by putting clay between two weights and seeing if the head-on collision looked more like a car going at 50 miles per hour or 100 miles per hour, and found that it looked like the car going 50.
Why it should be the same as 100
The reason Jamie said it would be the same as a car hitting a wall at 100 miles per hour is because of a principle in Physics called relativity. Now if you’ve heard of relativity before you’re probably thinking of Einstein’s Theory of Relativity, but actually the idea of relativity existed long before Einstein.
Imagine you’re driving down the highway at 80 miles per hour with a kid in the back seat throwing a ball in the air. From the perspective of the people in the car, the ball is going straight up and straight down. But if I’m standing on the side of the highway watching this it looks to me as if the ball is going in an arc, traveling at 80 miles per hour down the road.
This is why it’s called relativity, because our description of what’s happening is relative to our motion. To me standing still it looks like the ball’s moving, but to those in the car it looks like I’m moving. We have different reference frames.
In physics, it’s been proven that all inertial reference frames are valid. An inertial reference frame is just a reference frame where you’re either not moving or moving at a constant speed. Since both the ball in the car and me on the side of the highway are standing still/moving at a constant speed, we can both claim that we’re the ones standing still and the other one is moving.
So when we look at two cars driving towards each other you could say the crash is the same as if one car was sitting still and the other was going at 100 miles per hour.
Where they went wrong
So then why did the Mythbusters experiment show otherwise? If the two crashing into each other is the same as one crashing into a stationary object at twice the speed, why did their clay only compress half as much? The problem is that they changed something other than just whether the “car” was crashing into a stationary or moving object.
In the first experiment, the “car” on the right was crashing into a solid piece of steel. In the second one, it was crashing into another “car” that had some clay in the middle of it. This second piece of clay absorbed some of the impact in a way a solid piece of steel would not. And that, not whether it was moving, was the difference.
If the first experiment had the “car” hitting another stationary “car” with clay, they would have seen the same amount of compression both times. Alternately, if the second experiment had that solid piece of steel moving, they would have again seen the same amount of compression both times (assuming the steel weighed the same as the “car”).
Another way to think of it is that the total amount of clay compression was indeed greater in the 1x height when there were 2 “cars” instead of 1, since with 2 “cars” there were 2 pieces of clay being compressed. It’s like eating a piece of chocolate. Whether you eat the whole thing, or split it in half and share it with somebody else, the same amount of chocolate was consumed.