Re: A twist on the hourglass problem

[brian whatcott <inet@INTELLISYS.NET>]

At 06:35 11/3/99 -0800, Leigh wrote:

> The Flying Circus answer must have related to the steady flow regime.
> During that time the center of mass of a cylindrical hourglass will
> be falling at a constant speed. Since the hourglass is not accelerating
> during that time the weight will be the same as the weight with no sand
> flowing. There will be transients at the beginning of flow and the end
> of flow, and your student should examine the behaviour of the scale
> during those transients.
>
> My copy of TFCoP is at school or I'd check Jearl's answer. A few of his
> answers are not quite right. My explanation (the descending, non
> accelerating center of mass) works for me.
>
> Leigh

This is an appealing proposal - "Since the hourglass (CofG)is not
accelerating" its weight will be the same as the static weight.
It is in my view incorrect.
If we start with a cannister down which we drop a cannon ball
 - intuition assures us that the cannister weighs much less than
the combined weight of tube and ball - at least until the ball
reaches the base.

Let us proceed by small steps: with two balls dropped sequentially
the second starting when the first hits bottom - we see that the
loss of weight is only half the combined weight of balls.

With one hundred balls dropped sequentially in the same manner,
 we observe that the scale indicates only the loss of just one of
one hundred.
   We may (with our thermodynamicist's hat on) ignore individual
contributions and note simply that the center of gravity proceeds
 slowly from top to base at a constant rate - so there is no (gross)
acceleration - though as non-thermodynamicists we would easily see
 that an individual ball is indeed accelerating.

It is only this small accelerating sandfall that subtracts from the
 hour-glass's weight. And this, only so long as the sand still
accelerates (which a kind list contributor showed not so long ago,
may or may not happen near the base of the glass, depending on the
sand particle size and hence the air resistance which retards it.)

But re Walker's Flying Circus - he adopts your position- of an initial
transient and a terminal transient reasonably enough - but with no
loss of weight meanwhile
- which I hope will now give you pause for reconsideration.

   He references:
Reid W.P "Weight of an Hourglass" Am J Phys 35,351 (1967)

It would be instructive if a list member could quote Reid's argument
for 'no weight loss' to show me the error of my ways - or possibly his?

Respectfully
brian whatcott <inet@intellisys.net>
Altus OK