Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] bound vectors ... or not



Perhaps the way to demonstrate the fact that the torque is the same for
any point of action along the line of action of the force (a line
parallel to the the force vector and passing through the point of
application of the force) depicted in your diagram is to mount the disk
on a fixed torque wrench rather than an axle and attach one end of a
piece of string to the various points of the disk along the line of
action and have the string extend horizontally away from the disk, along
the line of action, before passing over a pulley to an object suspended
by the string. The fixed torque wrench gives same reading no matter
which point along the line of action the string is attached to.

Another interesting thing that you can do with a disk mounted on a
torque wrench is to weld nuts at various locations on the surface of the
disk and to each nut in turn apply a given couple, e.g with a T-handle
torque wrench. No matter where you apply the couple, the fixed torque
wrench gives the same reading, that of the given couple.

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Edmiston, Mike
Sent: Wednesday, September 08, 2010 1:49 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] bound vectors ... or not

I've been thinking about the critique of my constant-torque device
since Jeffrey Schnick and John Denker poked some holes in it.

I think the simplified, idealized situation I first observed in
Hibbeler's engineering physics book is correct, but my real device
suffers the usual failure of the simplified physics analysis to
describe a real device 100% accurately.

We're familiar with all those situations for which we ignore air
friction, for example when we introduce projectile motion. But in my
case the failure is more along the lines of some of the points raised
by others when discussing free-body-diagrams within our discussion on
vectors. The free-body-diagram does not truly represent the physical
reality. The forces acting on an object do not all attach at a common
point (often also considered to be the center-of-mass).

I hope the failure of the physical devise I described does not prevent
readers from understanding the simplified, idealized situation for
which any point of attachment along a line of action results in the
same torque on the object. To this end, I have created a second PDF
document that shows the simplified analysis in more detail than
provided in Hibbeler's text. This second document also points out the
things in the real device that prevent it from acting ideally.

I would also point out that in my first set of drawings I made the
slot
for the sliding pin longer than necessary. I think this led John and
Jeffrey to analyze the system over a greater angular displacement than
appropriate. The angular displacement can be very limited by how near
the line of action approaches the edge of the disk. I believe the
real
device follows the simplified physics much better as the line of
action
approaches being tangent to the edge of the disk, but this also
results
in very small range of motion. This also seems typical... the
analysis
is often reasonably valid only over some limited range.

Here is the link to the second drawings...

www.bluffton.edu/~edmistonm/ConstantTorque2.pdf


Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l