Re: rolling

[Brian Whatcott <betwys1@SBCGLOBAL.NET>]

If the drum moves L/2 wrt the ground,
and the board moves 3/2L wrt the ground,
how far does the board move with respect to the drum's top?
3/2L - L/2 = L

To repeat: The board does NOT move L with respect to the ground.
This is a difficulty that Justin shares with Daniel Crowe
But this was a physics puzzle, after all.

Here's an engineer's puzzle:
If you reasonably  suppose that the woman sensibly supports the longer
 unsupported end at all times, how far would she have walked?
.

Brian W

At 07:11 AM 2/4/2004, you wrote:
> I agree, as I stated in my original post, that the board moves a distance
> L with respect to the ground.  The question asks, "What length of board
> has rolled over the top of the drum?"  If the drum moves L/2 and the board
> L then the board moves L/2 w.r.t. the drum.  I am still confused about how
> the length "rolling over the top of the drum" could be L.
>
> In a message dated 2/3/2004 6:08:16 PM Eastern Standard Time,
> dcrowe@SOTC.ORG writes:
>
> >
> >
> > The board is always in contact with the top of the drum.
> > If the drum rolls without slipping, then the velocity
> > of the top of the drum is twice the velocity of the
> > center of the drum.  Therefore, the board moves twice
> > the distance covered by the center of the drum.  Note
> > that the board is in contact with different points on
> > the circumference of the drum as the drum rolls.
> >
> > Daniel Crowe
> > Oklahoma School of Science and Mathematics
> > Ardmore Regional Center
> > dcrowe@sotc.org
> >
> >
> > -----Original Message-----
> > =46rom: Justin Parke [mailto:FIZIX29@AOL.COM]
> > Sent: Tuesday, February 03, 2004 11:03 AM
> > To: PHYS-L@lists.nau.edu
> > Subject: rolling
> >
> >
> > I need some help with the following question from Halliday et al (6th=
> > ed.),
> > ch. 12 question 5:
> >
> > "A woman rolls a cylindrical drum, by means of a board on top, throug=
> > h the
> > distance L/2, which is half the board's length.  The drum rolls smoot=
> > hly, and
> > the board does not slide over the drum.
> > a)  What length of board has rolled over the top of the drum?
> > b)  How far has the woman walked?"
> >
> > The answers in the book are L and 1.5 L.  I am not sure I understand =
> > what is
> > meant by "what length of board has rolled over the top of the drum." =
> > It seems
> > to me that it should be L/2.  If the questions means how far has the =
> > board
> > moved with respect to the ground then I agree it is L.
> >
> > Answers in algebraic form (plus verbal explanations) are
> > preferable t=
> > o
> > strictly verbal arguments.
> >
> > Justin
>
> Justin Parke
> Oakland Mills High School
> Columbia, MD


Brian Whatcott    Altus OK    Eureka!