Okay, it's been way too long since I was in college, and I have a stupid physics question.
I have a choker/necklace. It is made out of many interconnected loops of metal (tin, aluminum, or some like of iron alloy I assume, but that is irrelevant).
I also have a table, the corner of which is, unsurprisingly, square. That is to say, it is a typical 90-degree angle. If I wrap the choker around the corner of the table (figure 2), I have observed that 100% of the time, gravity pulls the choker off the corner of the table. My question is--why?
I understand why the choker falls off if I drape it over the edge of the table (see figure 1). If the force of gravity on the length of choker that is hanging off the table (let us call this distance x) is greater than the frictional force of the length of the choker still on the surface of the table (let us call this distance (l - x)), it falls off, according to Coulomb's Law:
Fg > µFn
mgx > µmg(l - x) ,
x > µ(l - x) .
is the mass per unit length of the choker, x
is the length of the choker that is hanging from the table edge, and l
is the total length of the choker.
What I don't
understand is why the choker falls off the corner in figure 2. The force of gravity on the section of the choker underneath the table should be equal to the normal force on the section on the top of the table, right?