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# Re: rolling/erratum

I agree with Justin's statement given here below.
(And I agree with John M that my hasty post at lunchtime
was both confusing and erroneous in finger pointing both
Justin and Daniel)

Reviewing Justin's original statement of the problem,
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>"Halliday et al (5th? ed.),ch. 12 question 5:
>
> "A woman rolls a cylindrical drum, by means of a board on top,
>through the distance L/2, which is half the board's length.
> The drum rolls smoothly, 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 see that he can agree with Halliday's answer to a) but he can
reasonably defend L/2 for a)
So it is b) that concerns him.
In fact John M. says Halliday is wrong here.

In the same admirable manner as Justin, I rolled a ballpoint
with a rule, and found that the rule could be held at a variety
of positions during the roll. I think one would need to shift
the position at which the rule or board is held in order to have
moved 1.5L along the ground.
Values of L to 2L would be defensible in this manner, I suppose.
Hence in charity, I suggest b) is not constrained completely.

Still, a wonderful puzzle for exposing splendid, less than
gesundheit ..er.. I mean "gedanken experiment" fallacies.

Brian W

At 02:30 PM 2/4/2004, you wrote:
I performed this expermiment using a meterstick for the board and a
bicycle wheel for the drum. The initial condition of the meterstick was
the 0 cm mark directly over the hub of the wheel. When the wheel rolled
50 cm along the ground the 50 cm mark of the meterstick was directly over
the hub of the wheel. Thus the meterstick moved 50 cm + 50 cm = 1 m = L
along the ground. What am I missing? (By the way I supported the same
end the whole time)

Justin

In a message dated 2/4/2004 1:39:24 PM Eastern Standard Time,
betwys1@SBCGLOBAL.NET writes:

> 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

Justin Parke
Oakland Mills High School
Columbia, MD

Brian Whatcott Altus OK Eureka!