The MythBusters aren’t really doing it wrong, but they give me a chance to talk about some physics. In the latest show, they tested the myth that two phone books with their pages alternating were indestructible. To test this, they put the two phone books together and then pulled them apart in a sort of tug of war. Here is a diagram:
Looks great, what is wrong with this? The problem is that by pulling this way, the MythBusters produces 320 pounds of force on the book – but they could have done twice that. This really goes back to the old question: Which would produce a greater tension, two horses pulling in opposite directions, or one horse pulling on a rope tied to a tree. The answer is that both tensions are the same. However, many say that the two horses create a greater tension. The likely thinking in this “two horses are more” answer is that TWO things are doing something must be greater than ONE thing doing something. This reasoning fails because if you tie a rope to a tree, it is doing exactly the same thing the other horse doing: not moving.
Why? A force explanation follows:
Let me look at the forces on the phone book for the case where Adam and Jamie pull in opposite directions. The book is not changing in speed, so the total force on the book must be zero. Here is a force diagram of that situation.
First, let me point out that the two cables must pull slightly upward in order to balance the gravitational force. The horizontal components of tension in the two ropes is the same. What would change if Adam was replaced and his cable was tied to wall? The diagram would look exactly the same (except the word “Adam” would be replaced with the word “wall”). Really? A wall can exert a force? Sure. Have you ever tried to push on a wall? The wall pushes back.
What if Adam and Jamie pulled like this:
In this case, both Jamie and Adam would pull 320 lbs and the wall would pull the other way with 640 lbs of force. In the show, the MythBusters tried pulling the phone books apart with two cars pulling in opposite directions. They recorded a force of 4800 lbs. If they tied one rope to a tree (or rock) and had both cars pulling together, they could have achieved 9600 lbs. This would be enough to pull the two apart since they accomplished this with two military vehicles that registered 8000 lbs. But maybe the mythbusters are just smart enough to make it so that they HAD to use the military vehicles – that is what I would have done.