Physics and Fluids: Accelerating Particles in a Fluid

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Homework Help Overview

The discussion revolves around the dynamics of small particles moving through a fluid, specifically focusing on the forces acting on a particle experiencing drag proportional to its speed. The original poster presents a problem involving a particle of net weight W dropped in a fluid, aiming to determine the time required for it to reach 95% of its terminal velocity in terms of given variables.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the forces acting on the particle, including drag and gravitational forces. There is an ongoing clarification of the setup, with questions about the nature of the fluid and the assumptions regarding the system.

Discussion Status

The discussion is active, with participants engaging in identifying forces and formulating equations based on Newton's Second Law. Some guidance has been provided regarding the correct interpretation of forces, but no consensus or complete solution has emerged yet.

Contextual Notes

Participants are working under the assumption that the particle is falling in a fluid, and there is a focus on expressing the problem in terms of specific variables like k, W, and g. The nature of the fluid and the configuration of the system are still being clarified.

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Homework Statement



Very small particles moving in fluids are known to experience a drag force proportional to speed. Consider a particle of net weight W dropped in a fluid. The particle experiences a drag force, Fd = kV, where V is the particle speed. Determine the time required for the particle to accelerate from rest to 95% of its terminal velocity, Vt, in terms of k, W, and g.

Homework Equations



Newtons Second Law of motion, etc.

The Attempt at a Solution



I tried to sum forces, etc. but didn't really get anywhere...
 
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What forces act on the particle?
 
i wrote the question verbatim, so i will assume a drag force (and a force of flowing fluid?)
i can write the answer if it helps, but it's useless without the method.
 
allezfou said:
i wrote the question verbatim, so i will assume a drag force
Right. An expression for that is given.
(and a force of flowing fluid?)
That's the drag force.

What other force, also given, acts on the particle?
 
there is a force on the particle moving it forward and the drag force
 
allezfou said:
there is a force on the particle moving it forward
Yes. What is that force?
 
i don't know.
 
allezfou said:
i don't know.
Hint: It's one of the variables that your answer must be expressed in terms of. :wink:
 
gravity.
 
  • #10
allezfou said:
gravity.
Of course! Now write an equation using Newton's 2nd law.
 
  • #11
so am i assuming a vertical pipe with fluid in it?

kV-mg=ma. we don't want it in terms of acceleration so we use a=dV/dt.
 
  • #12
allezfou said:
so am i assuming a vertical pipe with fluid in it?
It's just a particle placed in some fluid and allowed to fall.
kV-mg=ma. we don't want it in terms of acceleration so we use a=dV/dt.
Good. I would switch the signs around, so that "down" is positive (since you know it's going to fall down).
 
  • #13
mg-kV=m dV/dt. the net weight is W, which is also mg.
W-kV=m dV/dt
 
  • #14
allezfou said:
mg-kV=m dV/dt. the net weight is W, which is also mg.
W-kV=m dV/dt
Good. Now just rearrange and integrate.
 

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