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 a

Question

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 If the maximum length L of this piece for which it does not break during the slide is k times l, find k.

TestHub · Accepted Answer

Breaking tension of the cable: τ = λ l g (weight of length l , λ = linear density) On the table, with overhang x : acceleration a = λ L λ xg ​ = L xg ​ Tension at the edge: T = λ ( L − x ) a = L λ g x ( L − x ) ​ , maximum at x = L /2 : T ma x ​ = 4 λ gL ​ For the cable not to break: 4 λ gL ​ ≤ λ l g ⇒ L = 4 l k = 4

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