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 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 Σ = m Then: -m v= m since: a = dv/dt then -m by integrating, we obtain the following expression: = voe Further, employing the rules of integration results to the following expression for position as a function of time x= (vo/ 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 Σ = m Then: -m since: a = dv/dt then 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 = vo- 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 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 Σ = m Then: -m v= m since: a = dv/dt then -m by integrating, we obtain the following expression: = voe Further, employing the rules of integration results to the following expression for position as a function of time x= (vo/ 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 Σ = m Then: -m since: a = dv/dt then 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 = vo- which, sows that velocity decreases in a linear maner.
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter6: Applications Of Newton’s Laws Of Motion
Section: Chapter Questions
Problem 62PQ
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