Re: [Phys-l] Linear Air Drag

["LaMontagne, Bob" <RLAMONT@providence.edu>]

Correct - If the balls are hollow then the weights might not be proportional to r^3 and the terminal speed would no longer be proportional to r^2. I carefully purchased solid balls of the same steel with a series of diameters from 1/16" to 8/16". This gives a 64:1 ratio between the fastest and slowest speeds - well beyond what is needed to verify the standard resistance formulas.

The assumption is that weight = resistance

4/3 pi rho_steel r^3 = 6 pi eta r v

hence v is proportional to r^2. Buoyancy will lower the speed but not affect the relationship.

Again, it's cheap, fun, and the results are amazingly good for a 1 hour student lab.

A weather balloon works great for air drag instead of viscous drag. If the balloon is weighed while inflated, the buoyancy is automatically accounted for. A drop from a good height ( > 10 m) shows that v is proportional to the square root of r as expected. The baloon is round enough and smooth enough so the drag coefficient of 0.5 give a good prediction of the fall time. The ballons I use are about 20" in diameter. These are the smaller red balloons - not the big white ones that are usually filled with hydrogen and expand to the size of a one or two car garage before they burst.

Bob at PC

________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Brian Whatcott [betwys1@sbcglobal.net]
Sent: Tuesday, November 03, 2009 8:12 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Linear Air Drag

LaMontagne, Bob wrote:
> Brian,
>
> I'm not sure what "generally" means in this case.
The general case I had in mind is the hollow ball bearing versus dense
solid metal ball bearing.
You will see that in these cases the drag is not simply proportional to
radius.
Or have I got it wrong?
> ... The terminal velocity is directly proportional to r^2 for the series of steel balls. The data form an amazingly straight line of slope 2 on a log-log plot.

For steel balls whose weight is a cubic function of radius, I'm pretty
sure you're right. For balls with other weight functions of radius, I
expect you're wrong.
But, I expect you would say the same?
> /snip/
> I don't think it's generally true however, that large balls drop faster
> in viscous liquids,  though denser or heavier balls would, wouldn't they?
>
> Brian W
>
> LaMontagne, Bob wrote:
>
> > /snip/ The relevant drag formula in this case is Resistance = C r v, where C is a constant and r is the radius of the sphere. The terminal speed becomes proportional to r^2. /snip/
> > Bob at PC

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l