2. The Falling Chain. A uniform chain of length 8 feet and weighing 2 pounds per

Question

2. The Falling Chain. A uniform chain of length 8 feet and weighing 2 pounds per foot Peg platform edge is loosely coiled at rest around a peg at the edge of a horizontal platform with 3 feet hanging over the edge. At time t 0 seconds the weight of the overhanging chain causes the chain on the table to uncoil smoothly and fall to the floor, which is more than 8 feet below. Assuming that the positive direction is downward, let r(t) denote the length of the overhanging chain at time t 0, and let v I'(t) be the velocity. (a) Ignoring all frictional forces, show that v v I) satisfies the differential equation (1) (b) Explain why I (0) 3, and also that when I 3 we have v 0. Use the integrating factor p (r,y) I to solve, by hand (i.e. no MAPLE), the differential equation (1) and determine v as a function of r. (c) Use (b) to determine the velocity as the last piece of chain exits the platform

Explanation / Answer

using bernolis threom we can find the differential eqn

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