# Homework Help: Physics and fluids

1. Sep 6, 2008

### allezfou

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Newtons Second Law of motion, etc.

3. The attempt at a solution

I tried to sum forces, etc. but didn't really get anywhere...

2. Sep 6, 2008

### Staff: Mentor

What forces act on the particle?

3. Sep 6, 2008

### allezfou

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.

4. Sep 6, 2008

### Staff: Mentor

Right. An expression for that is given.
That's the drag force.

What other force, also given, acts on the particle?

5. Sep 6, 2008

### allezfou

there is a force on the particle moving it forward and the drag force

6. Sep 6, 2008

### Staff: Mentor

Yes. What is that force?

7. Sep 6, 2008

i dont know.

8. Sep 6, 2008

### Staff: Mentor

Hint: It's one of the variables that your answer must be expressed in terms of.

9. Sep 6, 2008

### allezfou

gravity.

10. Sep 6, 2008

### Staff: Mentor

Of course! Now write an equation using Newton's 2nd law.

11. Sep 6, 2008

### allezfou

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. Sep 6, 2008

### Staff: Mentor

It's just a particle placed in some fluid and allowed to fall.
Good. I would switch the signs around, so that "down" is positive (since you know it's going to fall down).

13. Sep 6, 2008

### allezfou

mg-kV=m dV/dt. the net weight is W, which is also mg.
W-kV=m dV/dt

14. Sep 6, 2008

### Staff: Mentor

Good. Now just rearrange and integrate.