Date: Fri, 16 Feb 2001 16:27:50 -0500

Author: "Ramon O. Torres-Isea"

Subject: Re: physics question



If there is no net horizontal force on the cart-water system, the center of
mass will not move. If water collects to the right due to the drain hole, the
car must move to the left (to keep the center of mass at the same spot). If
the system is made up mostly of water, the drain hole will end up right below
the center of mass.

Ramón O. Torres-Isea
Adjunct Lecturer and Supervisor,
Advanced Physics Laboratories,
Department of Physics,
The University of Michigan,
Ann Arbor, MI

Phone: 734-764-3443

Russell Lawrence wrote:

> Greetings all,
> Can anyone tell me the answer to this question? I have 10 bucks riding on
> it with the chairman and another faculty member.
> A cart is sitting on frictionless horizontal rails. It is full of water
> and the water mass constitutes a large percentage of the total cart/water
> system mass. A drain hole and vertical drain pipe exists at the right end
> of, and is fixed to the cart. The drain guarentees that the water drains
> out vertically in the frame of the cart. The cart starts at rest and the
> cork in the drain is removed. Does the cart move? If it does move,
> describe the motion.
> The argument that it does not move is that there are no external forces on
> the cart and since the water drains out vertically, the sum of the internal
> forces are zero.
> The argument that it moves is based on the idea that the center of mass of
> the system must remain fixed.
> Notes that trouble me:
> If the cart does not move, then initially the center of mass of the system
> was somewhere at the center of the cart and after the water drains is at
> the right end of the cart-so the cm moved!
> If the cart moves, the water coming out during the motion has a horizontal
> component of velocity with respect to the earth frame (in this case the
> cart should move to the left). If this is true, then some of the water is
> travelling to the left (ie some of the cg) and so the cart, in order to
> keep the cg stationary would have to stop and turn around!???
> I thought this was a simple problem, and perhaps it is, but the more I
> think about it, I am not so sure. I would not post this if it did not
> cause deep concern about several demos I show often-fan and cart, balls on
> incline fixed to cart, etc. I would like to know exactly why the cart does
> not move-how you deal with the cg moving if it doesn't. And I would like
> to know the details of the motion(ie why it moves) if it does.
> I'll bet some of you have seen this and if so I am greatful for any
> references or explanations.
> Next, I will call the ACME supply company, get a bathtub, outboard motor,
> rollorskates and be able to propel myself like Wiley E. Coyote.
> Thanks for any assistance,
> russ
> "Nothing is good in moderation. You cannot know good in anything until you
> have torn the heart out of it by excess."
> -Oscar Wilde
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