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-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf
Of LaMontagne, Bob
Sent: Saturday, February 04, 2012 5:13 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] block sliding on a skateboard
-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Saturday, February 04, 2012 2:37 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] block sliding on a skatebo
..............................................................
................ snip
infinitely
These equations answer all parts of the question except:
How far does it slide relative to the ground?
This part of the question is not scalable. The answer is
sensitive to the functional form of the friction/velocityrelationship.
The block could travel anywhere from 0.5 m to infinity,depending on
as-yet unspecified details.usually a
In particular, sometimes sliding friction is approximated as being
independent of velocity (for nonzero velocity), but this is
terrible approximation. By way of contrast, note thatlubricants tend
to operate at very low Reynolds number, and produce dragthat scales
roughly like velocity to the first power. As a furthercontrast, at
high Reynolds numbers, fluid dynamic drag scales approximately likeeddy-current damping.
velocity squared. Or maybe the skateboard uses
Who knows. The problem is seriously underspecified.
[LaMontagne, Bob] Under the usual freshman physics
assumptions (friction constant and independent of velocity -
no pegs or other gimmicks - no wind, etc.) the block actually
travels a little LESS than 0.5 m relative to the ground while
it is sliding on the skateboard. As JD states, the forces on
the block and skateboard are equal and opposite - but since
the skateboard is accelerating, the block comes to the same
speed as the skateboard a little sooner than if the
skateboard couldn't roll.
Please correct my thinking on this if it is wrong. I will
need to revisit this with my students (big mea culpa).
Bob at PC
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