How Do You Model Air Resistance in Mechanics?

[raphile]

[SOLVED] Mechanics question - help please?

Hey, I've just signed up here, and not entirely sure if I'm posting in the right place. But I have a Mechanics question, which has confused me, so here goes:

Homework Statement

A bead of mass m is threaded onto a horizontal wire. When moving with speed u, the retarding force of air resistance is known to be ku^2 where k is a constant. Write down an equation of motion for the bead that describes the speed u in terms of the time t, and hence show that:

(m/u) = (m/u0) + kt

if u = u0 when t = 0.

Homework Equations

I guess F = ma ?

The Attempt at a Solution

Since the retarding force is given by ku^2 I tried letting a = (F/m) = (-ku^2)/m and then writing that u = u0 - (ktu^2)/m, because the speed should be the initial speed plus (acceleration x time) right? But when I re-arrange this equation to get something in terms of (m/u) it doesn't give me the right answer. Am I even on the right lines?

 

[Hootenanny]

Hey, I've just signed up here, and not entirely sure if I'm posting in the right place. But I have a Mechanics question, which has confused me, so here goes:

Homework Statement

A bead of mass m is threaded onto a horizontal wire. When moving with speed u, the retarding force of air resistance is known to be ku^2 where k is a constant. Write down an equation of motion for the bead that describes the speed u in terms of the time t, and hence show that:

(m/u) = (m/u0) + kt

if u = u0 when t = 0.

Homework Equations

I guess F = ma ?

The Attempt at a Solution

Since the retarding force is given by ku^2 I tried letting a = (F/m) = (-ku^2)/m and then writing that u = u0 - (ktu^2)/m, because the speed should be the initial speed plus (acceleration x time) right? But when I re-arrange this equation to get something in terms of (m/u) it doesn't give me the right answer. Am I even on the right lines?

Welcome to PF raphile,

This is indeed the right place. I'll give you a hint: You have correctly determined the acceleration, however what you actually have is a differential equation,

$$a = \frac{du}{dt} = -\frac{ku^2}{m}$$

 

[raphile]

Thanks, I've got it now!