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A uniform flexible chain of total length 2 m lies on a frictionless…
Question
A uniform flexible chain of total length 2 m lies on a frictionless horizontal table with a length of 0.5 m hanging vertically over the smooth edge; the rest lies on the table. The chain is released from rest and slides off. Taking g = 10 m/s^2, find the square of the speed of the chain (in m^2/s^2) at the instant the last link leaves the table edge.
✓ Verified answer: 18.75checked by our engine — not a guess
Step-by-step solution
Let lambda = M/L be the linear mass density and x the hanging length.
The driving force is lambda x g and the total moving mass is M = lambda L, so acceleration a = g x / L.
Writing a = v dv/dx: v dv = (g/L) x dx.
Integrate from x = 0.5 to x = L = 2: v^2/2 = (g/L)(L^2 - x0^2)/2, so v^2 = (g/L)(L^2 - x0^2) = (10/2)(4 - 0.25) = 5(3.75) = 18.75 m^2/s^2.
Final answer18.75
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