Re: Barn-Pole Nuts & Bolts contradiction
- From: sal <pragmatist@xxxxxxxxxx>
- Date: 02 Sep 2007 03:50:49 GMT
On Tue, 28 Aug 2007 16:42:01 +0200, harry wrote:
"David" <dseppala@xxxxxxxxxxxxx> wrote in message
news:5p58d3d6aiubpjio3g828vkldtfp3j6ej7@xxxxxxxxxx
This problem is the classic Barn Pole paradox with the barn replaced by
a long threaded nut and the pole replaced by a long threaded rod.
Let there be a threaded nut of length L and a threaded rod also of
length L as measured in a rest frame. Let each of these have N
threads.
Ok, so they fit *when in rest*. Now I hold my breath...
Now let the threaded rod and threaded nut move toward each other with
equal and opposite velocities as measured in this rest frame. And let
the threaded nut and the threaded rod each rotate such that when they
meet the rotation rate is such that threaded nut and threaded rod fit
perfectly and neither the rod nor the nut undergo any acceleration.
OK, so they are equally contracted as measured in this rest frame, so
yes they should fit.
How is this viewed using SR in the rest frame of the nut? In this
frame, per SR, the threaded rod spans a shorter distance than the
threaded nut. So that when the rod is completely encased by the nut,as
viewed in the inertial frame of the nut, the N threads of the rod span
less than the N threads of the nut. I don't see how this is physically
possible.
This one looks more interesting than the usual ones. :-)
Can someone explain this using SR concepts.
I'm lazy so, just like you I won't calculate but guess. We know that the
bolt looks very much twisted in the rest frame of the nut. In fact there
is only a single thread that is wound a number of times, depending on
the number of "twists". Thus the "N threads" claim does not apply to a
nut that looks additionally twisted due to motion: instead, the "number
of threads" will be counted differently. My guess is that this fully
accounts for the apparent impossibility to fit the bolt into the nut.
Cheers,
Harald
This is actually a rather cool problem if you try to picture it.
Picture the threads as seen by an observer in the stationary frame. How
fast do they seem to be moving?
As you turn a screw (or nut) the "surface features" -- the peaks and
valleys -- appear to move along the shaft. So, if we assume the nut and
the rod are turning in opposite directions at equal rotational speeds,
and that they're planning on fitting together when they meet, how fast
must their "surface features" appear to be moving?
Answer: They're _stationary_ in the "rest frame" in which the rod and
nut are moving toward each other. The threads on the rod are "crawling
back" along the rod, and the threads in the nut are "crawling back" along
the nut, just fast enough to exactly counter their mutual motion toward
each other.
Consequence: If we lay a (stationary) ruler along the rod in the rest
frame, the points at which the threads contact it will be FIXED -- they
won't move along the ruler. That's an absolute, and it'll be true in all
frames; the same is true, of course, of the nut. Those rulers, which we
have laid out in the rest frame, are stationary WRT each other, and will
be equally contracted all frames. The fact that the threads contact them
at _fixed_ points -- no clock dependency here! -- shows that the threads
of the nut and bolt must also be equally contracted in all frames.
More simply, the "surface features" on the rod and nut are moving at the
same speed in the rest frame ... and so, presumably, they must be moving
at the same speed in _all_ frames.
The rotation still adds a major "twist" to any attempt to work out the
solution in all its gory detail, but this seems like a plausible place to
start.
--
Nospam becomes physicsinsights to fix the email
I can be also contacted through http://www.physicsinsights.org
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