Re: work done by friction

[John Denker <jsd@MONMOUTH.COM>]

At 05:20 PM 10/26/99 +1000, Brian McInnes wrote:
>  Okay, I've
> been walking around the house wiping my hands across tables big and
> small ... and either my hand slips over
> the top or sticks to them intermittently.  In the former case the
> tables do not move, in the latter case they do start to move but when
> that happens there is no relative motion between hand and table.
> What am I missing here?

One thing you are missing is the nonlinear difference between static and
dynamic friction.  There are two possible scenarios:

1) You start out with smallish dynamic friction between hand and table-top,
and largeish static friction between floor and table-legs.  If you wipe
hard enough, you can get the table to accelerate. As soon as it does so,
i.e. as soon as some velocity develops, the friction between the floor and
table-legs drops to a smaller value (dynamic friction), further
acceleration is quite rapid.  The velocity quickly reaches hand-velocity
and stays there because of relatively large static friction between hand
and table-top.  This leaves only a rather short time during which the table
is both slipping and accelerating.  Perhaps the time was so short that you
missed seeing it.

Because of this effect, you will notice that my original suggestion called
for using a tea-tray with *wheels* as illustrated in
  http://www.monmouth.com/~jsd/how/htm/4forces.html#fig_table_friction
The idea is that the wheels will have incomparably less stiction than
ordinary table-legs.

2) It's also possible that pushed too hard and wiped from a standing start.
 In such a case there might be no phase (not even a short one) during which
the table is both slipping and accelerating.  To prevent this possibility,
make sure you make a "flying wipe" -- i.e. do it in such a way that your
hand is moving before it touches the tabletop.  Then if the table moves at
all you will know there must have been *some* period (however brief) when
it was both slipping and accelerating.

========

Combining the previous two ideas: You can *realy* get rid of static
friction by using a reasonbly massive cart with good wheels, so that it
will keep rolling for a few seconds.  Then while it is rolling, take
another flying swipe at it.  It will accelerate some more.  Do it again and
again, and observe that you put more and more energy into it using only
dynamic friction.

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com