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PSE Example 8.6 via Reduce

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112677] PSE Example 8.6 via Reduce
  • From: Eduardo Cavazos <wayo.cavazos at gmail.com>
  • Date: Sun, 26 Sep 2010 02:44:00 -0400 (EDT)

Hello,

Here's example 8.6 from PSE [1]:

    http://i.imgur.com/HJLqs.png

Here I'll be working with the "exercise" portion of the example; i.e.
the case where there is friction between point A and point B.

Use Reduce on the set of equations which describe the system between
point A and point B:

    http://i.imgur.com/PLWza.png

The result shows that vB is about 12.9.

Now use Reduce on the set of equations which describe the system
between point B and point C. Also, plug in our value of 'vB' manually:

    http://i.imgur.com/rujUz.png

We get the correct answer for dBC; i.e. about 40.3.

Above I solved the problem in "piecemeal" fashion; first I used Reduce
on the system from A to B and used the result from that to work with
the system from B to C, also using Reduce.

I don't have alot of experience with Reduce, but it seems like, in
theory, I should be able to throw the whole set of equations at Reduce
in one step, instead of in two steps. However, when I try to do so,
Mathematica seems to have trouble with it (at least on this system;
Pentium M with about 1.5GB RAM). So something along the lines of:

    http://i.imgur.com/2swfE.png

So my questions are... Is this too much for Reduce to handle? Would
you recommend the piecemeal method instead?

If you have suggestions for a way to better apply Mathematica to the
problem at hand, those are welcome also. :-)

Thanks!

Ed

1: Physics for Scientists and Engineers by Raymond A. Serway and John
W. Jewett


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