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Like friction, drag force opposes the motion of a particle in a fluid; however, drag force depends on the particle's velocity. Find the expression for the particle's velocity v(x) as a function of position at any point x 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. Assume that the particle is constrained to move in the x-axis only with an initial velocity vo. Solution: The net force along the x-axis is: ΣF-F = m For Blank 6 then: mv = m Since acceleration is the first time derivative of velocity a = dv/dt, mv = m We can eliminate time dt by expressing, the velocity on the left side of the equation as v = dx/dt. Manipulating the variables and simplifying, we arrive at the following expression = -k "Isolating" the infinitesimal velocity dx and integrating with respect to dx, we arrive at the following: = Vo- which shows that velocity decreases in a linear manner.

Like friction, drag force opposes the motion of a particle in a fluid; however, drag force depends on the particle's velocity. Find the expression for the particle's velocity v(x) as a function of position at any point x 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. Assume that the particle is constrained to move in the x-axis only with an initial velocity vo. Solution: The net force along the x-axis is: ΣF-F = m For Blank 6 then: mv = m Since acceleration is the first time derivative of velocity a = dv/dt, mv = m We can eliminate time dt by expressing, the velocity on the left side of the equation as v = dx/dt. Manipulating the variables and simplifying, we arrive at the following expression = -k "Isolating" the infinitesimal velocity dx and integrating with respect to dx, we arrive at the following: = Vo- which shows that velocity decreases in a linear manner.

College Physics
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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Problem Like friction, drag force opposes the motion of a particle in a fluid; however, drag force depends on the particle's velocity. Find the expression for the particle's velocity v(x) as a function of position at any point x in a fluid whose drag force is expressed as Fdrag= = kmy where k is a constant, m is the mass of the particle and v is its velocity. Assume that the particle is constrained to move in the x-axis only with an initial velocity vO- Solution: The net force along the x-axis is: ΣF - -F = m For Blank 6 then: mv = m Since acceleration is the first time derivative of velocity a = dv/dt, %3D mv = m We can eliminate time dt by expressing, the velocity on the left side of the equation as v = dx/dt. Manipulating the variables and simplifying, we arrive at the following expression = -k "Isolating" the infinitesimal velocity dx and integrating with respect to dx, we arrive at the following: = Vo - which shows that velocity decreases in a linear manner.
Transcribed Image Text:Problem Like friction, drag force opposes the motion of a particle in a fluid; however, drag force depends on the particle's velocity. Find the expression for the particle's velocity v(x) as a function of position at any point x in a fluid whose drag force is expressed as Fdrag= = kmy where k is a constant, m is the mass of the particle and v is its velocity. Assume that the particle is constrained to move in the x-axis only with an initial velocity vO- Solution: The net force along the x-axis is: ΣF - -F = m For Blank 6 then: mv = m Since acceleration is the first time derivative of velocity a = dv/dt, %3D mv = m We can eliminate time dt by expressing, the velocity on the left side of the equation as v = dx/dt. Manipulating the variables and simplifying, we arrive at the following expression = -k "Isolating" the infinitesimal velocity dx and integrating with respect to dx, we arrive at the following: = Vo - which shows that velocity decreases in a linear manner.
Calculated Answers Express your answers without rounding off and without scientific notation unless instructed otherwise. Do not include the units. Multiple Blanks Write powers or subscript as is. Ex: Use b2 if you mean b2 or b2 Write transcendental functions as is. Ex. Use costheta if you mean cose. Spell out Greek letters. Ex: Use pi if you mean A Write answers without spaces. Ex: Use 2epsilonOr3 if you mean 2e r3. Write fractions with a slash. Ex: Use 1/2 if you mean
Transcribed Image Text:Calculated Answers Express your answers without rounding off and without scientific notation unless instructed otherwise. Do not include the units. Multiple Blanks Write powers or subscript as is. Ex: Use b2 if you mean b2 or b2 Write transcendental functions as is. Ex. Use costheta if you mean cose. Spell out Greek letters. Ex: Use pi if you mean A Write answers without spaces. Ex: Use 2epsilonOr3 if you mean 2e r3. Write fractions with a slash. Ex: Use 1/2 if you mean
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