Re: Dumb wheel physics question

On 29 Mar 2007 22:49:14 -0700, "Ron Ruff" <rruffrruff@xxxxxxxxx>
wrote:

On Mar 29, 7:30 pm, carlfo...@xxxxxxxxxxx wrote:
Until I wonder if the extra energy is supplied by the extra
gravitational pull on the extra mass, so it all cancels out, and hoops
of the same dimensions (and CRR) will accelerate uniformly down a
slope in a vacuum.

Yep. Things are a lot simpler in a vacuum. The equation I used for
calculating the transient motion for a cyclist is:

a=P/Mi/V- CdA*Da*V^2/2/Mi- g*G*M/Mi- g*Crr*M/Mi

In a vacuum, and no power input, the only terms left are:

a= -g*G*M/Mi- g*Crr*M/Mi where g is gravitational acceleration, G is
the grade, M is the static mass, and Mi the inertial mass. So the
acceleration will be the same if M/Mi is the same for both.

So then I wonder if that means that a heavy enough wheel would refuse
to move at all down the slope, while a light enough wheel would reach
the speed of light. (I'm pretty sure that this logic must have a
gaping hole in it somewhere, but I'm floundering.)

They will both reach the speed of light at infinity.

I'm beginning to wonder if my friend has some famous damn experiment
up his sleeve. The only demonstration that I remember showed that
solid spheres roll faster down the same slope than solid disks, which
in turn roll faster than hoops--nothing about whether a denser hoop
rolls faster, slower, or the same speed down a hill as lighter hoop.

Make sure you get the parameters of the thought experiment clear
before you lay your money down, though...

Dear Ron,

I'm not even sure how I think I'm describing it.

But my friend's idea about same-dimension steel versus aluminum
rolling down a steady slope in a vacuum from the start seems to be
pretty close.

The same dimensions would idealize the distances and sizes, the vacuum
would remove pesky wind drag considerations, and the question would be
reduced (I think) down to heavier versus lighter hoops of the same
size rolling downhill.

You're saying (I think) that they'd accelerate from a standing start
at the same speed, just like a BB and a cannonball dropped in a
vacuum, right?

Sorry if I'm misunderstanding or confusing things.

Cheers,

Carl Fogel
.

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