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[Phys-L] Re: Free body diagram misconception



The fundamental problem with your analysis is that you have miss read
Newton's second law. The F is the net force acting on the body of
interest. If the body of interest is object 1 then the applied force
is of interest. However since the body of interest is 2 (and you
know that because that is the mass you used on the right side of the
equation), and the force acts on 1, it is not considered.
Newton's second law, assuming a constant mass is The net force acting
on a body is the mass of that body times its acceleration of that
body. More generally the net force acting on a body is the change in
momentum of that body. If you don't keep the notion of "acting on a
body" clear, you can run into all sorts of problems with N1 and N3.

So as was mentioned elsewhere, the only horizontal force acting on 2
if the one
arrising from friction which you cannot predict directly as mentioned
in another note. Rather you can infer it by finding the acceleration
of the "block 1, block 2" system and then checking to see if that is
the acceleration of block 1 also.

It may not be, since you may have exceeded the maximum static
friction forcel by block 2 on block 1 in which case, block 1 will
slide with respect to block 2. In that case you can infer that the
frictional force by block 1 on 2 and 2 on 1 is the kinetic friction
force, and everything needs to be recalculated.

Seems to me there could be region of instability in which the blocks
may display a macroscopic "stick and slide" motion which as I recall
is what microscopically happens when objects apparently slide
continuously over each other, but that is another issue.

If you want to practice drawing free body drawings, take a look at
Freebody, a piece of software available from the AAPT.

joe

Joseph J. Bellina, Jr. Ph.D.
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556

On Oct 20, 2005, at 9:07 PM, Gene Gordon wrote:

Hello all, I have a strange physics question that the 5 physics
teachers at our high school sat and pondered today. We have started
teaching AP-C physics and the teacher for this new course came to us
with a variation to a question from the book. Here it is.

Block 1 is at rest atop Block 2. Block 2 rests atop a frictionless
surface. A force is applied to Block 1 pulling it to the right. The
coefficient of friction between blocks 1&2 is some non-zero value less
than 1. What is the Net force equation for Block 2?

We drew the free body diagrams for both blocks and came up with the
following equation for Block 2.

(mu)m1g - F(pull) = m2a2

Now all of us agreed on this, but we also saw a problem. This means
that there is some value for the force of the pull that Block 2
will not
move. However it is on a frictionless surface and IF they were
connected the Frictional component would disappear - thus the object
would accelerate. What is wrong with our reasoning? Did we make
a bad
assumption somewhere?

I love these problems but it is driving me bonkers since I know that I
am forgetting something fundamental --- Block 2 should accelerate for
ANY force pulling on it if it is on a frictionless surface.

Thanks in advance for any help.


Gene Gordon