Did you know that if you place a napkin on a table, then put a glass on the napkin and pull the napkin rapidly, the glass will stay on the table? Of course you did! But how hard (or, rather, how fast) do you actually have to pull the napkin in order to, ahem, pull off the trick?
Let us suppose that the part of the napkin laid on the table has a length d, and the glass is placed on the napkin a distance x from the edge of the table (the size of the glass is small compared to x). The coefficient of kinetic friction between the glass and the napkin is μ. Assume that you begin to pull the napkin horizontally at a constant speed v. What minimum value of v would leave the glass on the table? Assume that once the glass touches...
