Yes, I am going to talk about the MythBusters latest duct tape episode. A couple of pre-post points:
- They call it “duct” tape. I call it duck tape. It doesn’t work very well with ducts. Also, it is good for water proofing stuff – you know like a duck. For the rest of this post, I am calling it duck tape. (Wikipedia agrees there is some naming problem)
- You know I love the MythBusters – right? I hope you don’t think I sit around waiting for them to make a mistake so I can pounce on them (I save that for ESPN Sport Science). In this case, they just made a small mistake. A mistake that can be used to show something about physics.
- Duck tape bridge = awesome
Ok, on to the small mistake. One of the things the MythBusters were testing with duck tape was the idea that you could tape a car to a light pole so it couldn’t move. To do this, Tory and Grant used a force gauge to measure how much the car in question could pull. They got about 1300 lbs. Also, they knew from Jamie and Adam that one strand of duck tape would break around 67 lbs. So, how much tape do you need? They said 20 strands because 20 x 67 lbs = 1340 lbs. Ah HA! There is the problem. Really. Let me draw a diagram of the car looking down from above.
To first approximation, let me assume that the tape is pulling in the exact opposite direction the car is trying to drive. In that case, I can draw the following force diagram:
If the car is in equilibrium, then in the direction the car is trying to go the following is true:
So, if the frictional force on the car is 1300 pounds, then the total force each tape must exert would be 650 pounds. How many layers of tape would that need?
Not 20. But, to be honest, I don’t really know how they were counting. Maybe they counted both sides to get to their 20 layers. Ok, now for something a little different. What if I consider that they are at an angle? Here is the force diagram with the tapes at an angle.
Now in the direction the car is trying to go, the following must be true:
Notice that I am call Ftape-1 the force 1 layer of tape can exert on the car and n is the number of layers. What if I want n to be 20. What would theta have to be?
Maybe this is what the MythBusters were doing (they were right about the colliding two objects – remember?)