Re: rolling/erratum

[Brian Whatcott <betwys1@SBCGLOBAL.NET>]

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!