Given the nature of the title of the problem, I need hints to guide me in the right direction. I am sort of lost.
A student has a large quantity of a flexible cable. If she cuts a piece of that cable and hangs it vertically, the longest piece that does not break under its own weight is l. The student then cuts another piece and places it on a horizontal smooth table. A small part of that cable hangs over the edge so that the cable begins to slide down after being released. How long (L) can this piece be so it does not break during this slide?
F = ma and F = clg for vertical cable
a = l1g/(l1 + l2 = L) where l1 is the part of the cable on the horizontal table and l2 is the part of the cable hanging off the horizontal table. Similar to pulley and string situation.
The Attempt at a Solution
I set F = clg and F = m [l1g/(l1 + l2) =L] equal to each other and got L = ml2g/ clg.