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, aswell as the constant g.h =(b) The cylinder is now displaced a distance y from the equilibrium position, such that Jyl < 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 Tof the cylinder's oscillations? Your answer should use only the given symbols M, r, L, y, and p as necessary, as well asthe 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 equllibrium, 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. (b) The cylinder is now displaced a distance y from the equilibrium position, such that lyl

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 equllibrium, 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. (b) The cylinder is now displaced a distance y from the equilibrium position, such that lyl

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter15: Fluids

Section: Chapter Questions

Problem 46PQ

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Concept explainers

Density of Solids

The density of a substance refers to how much matter is present in a given amount of space. It is expressed as the ratio of the mass of the substance to its volume.

Question

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 Jyl < 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 Tof 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 =

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