An elastic string has a force constant k and mass m. The string hangs vertically, and a block of an unknown mass is attached to its bottom end. It is known that the mass of the block is much greater t

Question

An elastic string has a force constant k and mass m. The string hangs vertically, and a block of an unknown mass is attached to its bottom end. It is known that the mass of the block is much greater than that of the string. The hanging block stretches the string to twice its relaxed length. How long (t) would it take for a lowamplitude transverse pulse to travel the length of the string stretched by the hanging block? m = 1 kg , k = 2 1 ​ N/m.

TestHub · Accepted Answer

Block mass ≫ string mass, so tension is uniform: T = k Δ L = k L 0 ​ (string stretched from L 0 ​ to 2 L 0 ​ ). Stretched linear density: μ = 2 L 0 ​ m ​ . Pulse speed: v = T / μ ​ = m 2 k L 0 2 ​ ​ ​ = L 0 ​ m 2 k ​ ​ . t = v 2 L 0 ​ ​ = k 2 m ​ ​ = 1/2 2 × 1 ​ ​ = 2 s .

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