For Blank 6 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 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.

For Blank 6 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 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

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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Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”

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just fill up the missing parts or the blanks

For Blank 6
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
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.

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