Re: correct answer

[Bob Sciamanda <sciamanda@worldnet.att.net>]

Bob Sciamanda wrote:
> This is like a conveyor belt picking up additional mass:  energy
> is dissipated!  But that is no problem to the Work Energy theorem
> because it is not concerned with energy conservation.
>
> If you integrate the applied force over the CENTER OF MASS
> coordinate (NOT the "point of application")  you will get the
> change in the system C.M. kinetic energy, which is what the
> Work Energy theorem requires.
>
> Conservation of energy is another story!

In the light of other comments, let me add that (as in the 
conveyor belt taking on additional mass) I view this as a 
series of totally inelastic collisions as each "link" is 
brought up to speed.  A totally inelastic collision 
occurs whenever two masses, initially at different speeds, 
interact so as to achieve a common speed ; this mandates 
a definite loss of kinetic energy.  This dissipated energy  
is made up by the motor driving the conveyor belt, or by 
the agent pulling the chain.  

I agree that the fire hose is not a good embodiment of this 
idealization. But a chain of links allows each link in turn to 
be brought up to speed while the remaining coil remains at 
rest, as envisioned in my idealization. Then this problem is 
"identical" to the motor driven conveyor belt passing under a 
dispenser of sand which continually increases the amount of 
moving mass, necessitating inelestic interactions.

(Note: the work integral over the trajectory of the CM is 
worth doing explicitly.)

-- 
Bob Sciamanda				sciamanda@edinboro.edu
Dept of Physics				sciamanda@worldnet.att.net
Edinboro Univ of PA			http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA				(814)838-7185