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Bob's answer is of course correct for the usual friction model. I don't think that it deserves the usual dose of physics attitude that it received.
-----Original Message-----.............................................................................. snip
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
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 infinitely sensitive to
the functional form of the friction/velocity relationship.
The block could travel anywhere from 0.5 m to infinity, depending on as-yet
unspecified details.
In particular, sometimes sliding friction is approximated as being
independent of velocity (for nonzero velocity), but this is usually a terrible
approximation. By way of contrast, note that lubricants tend to operate at
very low Reynolds number, and produce drag that scales roughly like velocity
to the first power. As a further contrast, at high Reynolds numbers, fluid
dynamic drag scales approximately like velocity squared. Or maybe the
skateboard uses eddy-current damping.
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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