(a) Determine a differential equation for the velocity v(t) of a massm sinking in water that imparts a resistance proportional to the square of the instantaneous velocity (with a constant of proportionality k > 0) and also exerts ar upward buoyant force whose magnitude is given by Archimedes' principle, which states that the upward buoyant force has magnitude equal to the weight of the water displaced. Assume that the positive direction is downward. (L be the volume of the object, p the weight density of water, and g the acceleration due to gravity.) dv =g- ku dt (b) Solve the differential equation in part (a). w(t) = (C) Determine the limiting, terminal, velocity of the sinking mass. mg k lim v(t) =

(a) Determine a differential equation for the velocity v(t) of a massm sinking in water that imparts a resistance proportional to the square of the instantaneous velocity (with a constant of proportionality k > 0) and also exerts ar upward buoyant force whose magnitude is given by Archimedes' principle, which states that the upward buoyant force has magnitude equal to the weight of the water displaced. Assume that the positive direction is downward. (L be the volume of the object, p the weight density of water, and g the acceleration due to gravity.) dv =g- ku dt (b) Solve the differential equation in part (a). w(t) = (C) Determine the limiting, terminal, velocity of the sinking mass. mg k lim v(t) =

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter14: Fluid Mechanics

Section: Chapter Questions

Problem 93P: A spherical particle falling at a terminal speed in a liquid must have the gravitational force...

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