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Re: rolling

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
> -----Original Message-----
> =46rom: Justin Parke [mailto:FIZIX29@AOL.COM]
> Sent: Tuesday, February 03, 2004 11:03 AM
> To:
> 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!