Re: correct answer

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Thu, 9 Oct 1997, roger haar wrote:

> 	I think I see a flaw in this logic.  I think
>
> 		dx = v_ave dt = v/2 dt.  
>
> Remeber the segment of hose is not moving before the force 
> is applied and a time dt later is moving with velocity v.

Uh-oh, some differential nightmares lurking here.  The above implies that
each element has a (constant) acceleration of v/dt as it is brought to
speed v in time dt. So my next question is, "What is dt?" 

We assume an inextensible hose to make the problem tractable. In that case
each infinitesimal element is brought *instantaneously* to speed v when
its time comes.  If there is any finite acceleration going on, then the
hose is extensible and stretching.  If the hose is extensible, the problem
gets *much* harder since we cannot easily determine the force acting on
the leading end as Mark did.

On the other hand, it is precisely the extensible nature of real hoses and
the need to dissipate oscillations that will be set up in the process of
pulling on them, that explains the "paradox."  In the inextensible
extreme, this dissipation happens instantaneously and locally within each
infinitesimal element as it is brought up to speed. 

John
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