Problem Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as Fdrag = kmv where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling at with a velocity vo. Solution: a) To solve for the position as a function of time x(t), we construct the net force in the x-axis as Then: -m V = m since: a = dv/dt then -m V = m by integrating, we obtain the following expression: = vge Further, employing the rules of integration results to the following expression for position as a function of time x= (vo e as t+ 0, the position becomes x = vo/k b} To solve for the velocity as a function of position v(x), we construct the net force in the x-axis as follows E F=F = m Then: -m V = m since: a = dv/dt then -m V = m We can eliminate time by expressing, the velocity on the left side of the equation as V = dx/dt Then, we arrive at the following expression = -k By integrating and applying the limits, we arrive at the following = V0 - which, sows that velocity decreases in a linear maner.

Problem Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as Fdrag = kmv where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling at with a velocity vo. Solution: a) To solve for the position as a function of time x(t), we construct the net force in the x-axis as Then: -m V = m since: a = dv/dt then -m V = m by integrating, we obtain the following expression: = vge Further, employing the rules of integration results to the following expression for position as a function of time x= (vo e as t+ 0, the position becomes x = vo/k b} To solve for the velocity as a function of position v(x), we construct the net force in the x-axis as follows E F=F = m Then: -m V = m since: a = dv/dt then -m V = m We can eliminate time by expressing, the velocity on the left side of the equation as V = dx/dt Then, we arrive at the following expression = -k By integrating and applying the limits, we arrive at the following = V0 - which, sows that velocity decreases in a linear maner.

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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