A cylinder with a mass M and radius r is floating in a pool of liquid. The cylinder is weighted on one end so that the axis of the cylinder stands vertically. The total length of the cylinder is L. The density of the fluid is p. (a) When the cylinder is in equilibrium, a portion of it is submerged in the liquid. What is the vertical length h of this submerged portion? Your answer should use only the given symbols M, r, L, and p as necessary, as well as the constant g. h = (b) The cylinder is now displaced a distance y from the equilibrium position, such that |ly] < h, and released from rest. Let the +y-axis be upward, so that if the cylinder is pulled up, y is positive, but if it is pushed down, y is negative. Immediately after it is released, what is the y-component of the acceleration a, of the cylinder? Your answer should use only the given symbols M, r, L, y, and p as necessary, as well as the constant g. (Indicate the direction with the sign of your answer.) ay = (c) The result of part (b) implies the cylinder is now in simple harmonic motion. What is the period T of the cylinder's oscillations? Your answer should use only the given symbols M, r, L, y, and p as necessary, as well as the constant g. T =

A cylinder with a mass M and radius r is floating in a pool of liquid. The cylinder is weighted on one end so that the axis of the cylinder stands vertically. The total length of the cylinder is L. The density of the fluid is p. (a) When the cylinder is in equilibrium, a portion of it is submerged in the liquid. What is the vertical length h of this submerged portion? Your answer should use only the given symbols M, r, L, and p as necessary, as well as the constant g. h = (b) The cylinder is now displaced a distance y from the equilibrium position, such that |ly] < h, and released from rest. Let the +y-axis be upward, so that if the cylinder is pulled up, y is positive, but if it is pushed down, y is negative. Immediately after it is released, what is the y-component of the acceleration a, of the cylinder? Your answer should use only the given symbols M, r, L, y, and p as necessary, as well as the constant g. (Indicate the direction with the sign of your answer.) ay = (c) The result of part (b) implies the cylinder is now in simple harmonic motion. What is the period T of the cylinder's oscillations? Your answer should use only the given symbols M, r, L, y, and p as necessary, as well as the constant g. T =

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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6v За R EIND: V, I, & R 5a エ 12v