The other myth the MythBusters looked at last week was the phrase "knock your socks off" (along with the dropping and shooting a bullet myth). But before that, let me complain.
Maybe it is just me, but I totally cringe when these guys use the word 'force'. Force probably isn't the best term to use to describe a collision especially when you are talking about one of the objects. "oh, we will just give this object some more force to impact with that other object". Force is not a property of an object, but rather an interaction between two objects. When two things collide, you really need to consider force AND time (or you could argue force and distance - but it is NOT just force). Imagine I drop a glass on a pillow and a hard floor (from the same height). If I were able to make a plot of force vs. time for these two while they were hitting the ground, it might look like this:
The point is that these two glasses have the same properties, but very different forces in the interactions. Ok. I am done with that.
Knocking socks off
The MythBusters' basic approach was to put socks on their dummy (Buster) and then make him accelerate by hitting him. The idea is that for some high accelerations, his socks might come off. Here is a diagram of Buster and his socks while he is accelerating. I am just going to draw the forces on his socks.
In this case, the object of interest is the sock. The following must be true for the forces on the sock:
As long as the friction force is large enough to make this true, the socks will have the same acceleration as the person and stay on the feet. Note, the m is the mass of the socks. This seems straight forward enough. If I look at the y-direction and solve for the acceleration:
All I need is the maximum friction force keeping the socks on and mass of the sock. Then I can calculate the acceleration. Let me do this as a spreadsheet so you can make your own guesses as well. I will start with a sock mass of 100 grams and a frictional force of 10 Newtons (thinking how much mass you would have to put on the sock to make it slip off). If you don't like these numbers, you know what to do.
That gives an acceleration of 90 m/s2 or about 9 g's. I guess that is possible. However, I think my initial estimates may be off. What is the mass of a sock? How hard is it to take off? These (as I am sure you will agree) are quite varied. I have a pair of loose wool socks that are quite easy to pull off.
1) Is Buster pointing his toes straight down? If not, we need to worry about the frictional force increasing while he's accelerating, and apply some cosines to figure out the reduction in the force that's going to sock removal.
2) By pulling the strechy socks I'm wearing at the moment, I'd ballpark the force for sock removal (to remove the entire sock at once, as opposed to pushing it down from the top over the ankle) at around 20 pounds, or around 100 N. A quick trip to the scale puts the same sock (cotton, ankle-height) at 25 grams. If we assume toes down, that would push the acceleration up to around 400 g's. Even applied for the brief time necessary to strip off a pair of socks, I'd expect that to be lethal. Your sock mileage may vary, however.