Re: PSE Example 8.6 via Reduce

*To*: mathgroup at smc.vnet.net*Subject*: [mg112882] Re: PSE Example 8.6 via Reduce*From*: Eduardo Cavazos <wayo.cavazos at gmail.com>*Date*: Tue, 5 Oct 2010 05:31:45 -0400 (EDT)*References*: <i7mq41$ovh$1@smc.vnet.net> <i8c8t0$g8f$1@smc.vnet.net>

On Oct 4, 5:05 am, Eduardo Cavazos <wayo.cava... at gmail.com> wrote: > On Sep 26, 1:44 am, Eduardo Cavazos <wayo.cava... at gmail.com> wrote: > > > > > 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? > > In particular, the trouble is that the computation ran over 3 hours > without completing. When I split up the problem, each piece takes a > few seconds. Here's the code for the non piecemeal approach: Timing[Reduce[{ Subscript[\[CapitalEpsilon], A] == Subscript[K, A] + Subscript[U, A], Subscript[K, A] == 1/2 m*Subscript[v, A]^2, Subscript[U, A] == m*g*Subscript[y, A], Subscript[\[CapitalEpsilon], B] == Subscript[K, B] + Subscript[U, B], Subscript[K, B] == 1/2 m*Subscript[v, B]^2, Subscript[U, B] == m*g*Subscript[y, B], Subscript[\[CapitalDelta]E, AB] == Subscript[\[CapitalEpsilon], B] - Subscript[\[CapitalEpsilon], A], Subscript[\[CapitalDelta]E, AB] == -Subscript[\[CapitalEpsilon], frictionAB], Subscript[\[CapitalEpsilon], frictionAB] == Subscript[f, kAB]*Subscript[d, AB], Subscript[f, kAB] == Subscript[\[Mu], k]*Subscript[n, AB], Subscript[n, AB] == m*g*Cos[\[Theta]], Sin[\[Theta]] == Subscript[y, A]/Subscript[d, AB], Subscript[d, AB] > 0, Subscript[\[CapitalEpsilon], frictionAB] > 0, Subscript[v, B] > 0, Subscript[\[CapitalEpsilon], B] == Subscript[K, B] + Subscript[U, B], Subscript[K, B] == 1/2 m*Subscript[v, B]^2, Subscript[U, B] == m*g*Subscript[y, B], Subscript[\[CapitalEpsilon], C] == Subscript[K, C] + Subscript[U, C], Subscript[K, C] == 1/2 m*Subscript[v, C]^2, Subscript[U, C] == m*g*Subscript[y, C], Subscript[\[CapitalDelta]E, BC] == Subscript[\[CapitalEpsilon], C] - Subscript[\[CapitalEpsilon], B], Subscript[\[CapitalDelta]E, BC] == -Subscript[\[CapitalEpsilon], frictionBC], Subscript[\[CapitalEpsilon], frictionBC] == Subscript[f, kBC]*Subscript[d, BC], Subscript[f, kBC] == Subscript[\[Mu], k]*Subscript[n, BC], Subscript[n, BC] == m*g, Subscript[d, BC] > 0, Subscript[\[CapitalEpsilon], frictionBC] > 0 } /. { Subscript[y, A] -> 20, Subscript[v, A] -> 0, Subscript[y, B] -> 0, Subscript[y, C] -> 0, Subscript[v, C] -> 0, Subscript[\[Mu], k] -> 0.210, g -> 9.8, \[Theta] -> 20 Degree }, Reals]] Ed