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Block A is resting on Block B. Bock A weighs 50 lbf. and is teathered to a wall. Block B weighs 80 lbf.and is resting on Block C that weighs 100 lbf. ( which is resting on the ground). The coefficients of friction between all the mating surfaces are the same ( 0.30).
A massless rope is tied to Block B.
How much force can be applied to the rope ( horizontally) before equilibrium is disturbed.
I'm not really interested in the solution ( I already can solve it), but I am interested in understanding the answer to the following question:
If only one possible scenario "can and will" physically occur, why is there not a way to go directly to that solution? That is, you must treat two different scenarios equally in the mechanics: Namely Block B slides out from between Blocks A & C (scenario 1), and Blocks B & C moves out from under A (scenario 2). Is it all just related to the extra degree of freedom? Is there a direct solution to this in the Calculus of Variations or something similar?
Originally posted by joe shmoIt seems simply a comparison of friction forces.
Block A is resting on Block B. Bock A weighs 50 lbf. and is teathered to a wall. Block B weighs 80 lbf.and is resting on Block C that weighs 100 lbf. ( which is resting on the ground). The coefficients of friction between all the mating surfaces are the same ( 0.30).
A massless rope is tied to Block B.
How much force can be applied to the rope ( h ...[text shortened]... freedom? Is there a direct solution to this in the Calculus of Variations or something similar?
Which is greater - friction between B and C, or friction between C and ground? Whichever is less is where the slippage will take place.
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Originally posted by AThousandYoungEffectively...Yes that is this case for this example. You are missing my point though. In reality, only one of the scenarios will occur for a certain set of parameters, but in order to solve it (with methods that I'm aware of) we need to perform the analysis for the other possible scenarios, and "choose" the minimum which satisfies the conditions. Nature doesn't do this ( as far as we are currently aware of ), and I'm interpreting it as "Mechanics" alone is insufficient to handle this particular type of determinism.
It seems simply a comparison of friction forces.
Which is greater - friction between B and C, or friction between C and ground? Whichever is less is where the slippage will take place.
That is why I mentioned the Calculus of Variations, it is designed to "choose minimums" with a single stand alone analysis ( like "choosing" the line as the shortest way to connect two points in space) out of an infinite number of other possible curves). So, can it be used in some form to determine the minimum directly in this type of scenario?
Originally posted by joe shmoNot consciously, no, but I don't think that was a condition in your original post. Nature could certainly be said to 'calculate' and move according to rules that govern the system. Its mostly just a matter of forces building up until they overcome friction and the location with the lowest friction gives first.
Nature "calculates" all possibilities and then consciously "chooses" the the extrema or state which satisfies the the system?
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I think we are confusing the map and the territory here.
What's happening in reality is a bunch of electrons and quarks interacting via forces.
Or perhaps its a bunch of vibrating strings interacting via whatever the hell string theory
says the interact by. Or maybe it's something deeper than that.
The behaviour of the blocks and rope and floor and wall are all simply governed in nature
by the ground state reality [whatever that is]. Countless numbers of interactions between
the ground-state bits that make up reality.
EVERYTHING we do is make up mathematical approximations and simplifications that
allow us to model and predict what is going to happen. None of those models are actually
reality, they are simply our maps to understanding it.
And we use different scale maps, different models, to deal with different scale problems.
We can't solve the block problem via quantum mechanics [or string theory, or whatever]
because there is no possible or practical way we could solve equations for every possible
quark and electron and photon that makes up the blocks, wall, floor, and rope.
We can't do it the way 'nature' does.
What we can do is make up simple mathematical approximations, that allow us to answer the
question as to what will occur.
In this case a simple calculation to tell which slipping point is higher will answer the question.
And I don't see why we need anything more complex than that.
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Originally posted by googlefudge"And I don't see why we need anything more complex than that."
I think we are confusing the map and the territory here.
What's happening in reality is a bunch of electrons and quarks interacting via forces.
Or perhaps its a bunch of vibrating strings interacting via whatever the hell string theory
says the interact by. Or maybe it's something deeper than that.
The behaviour of the blocks and rope and floor ...[text shortened]... higher will answer the question.
And I don't see why we need anything more complex than that.
I didn't say we "need" a different way to do it. I just asked if there "is" a different way to do it. I (and I think most others) would prefer to have the machinery and not use it, than not have it at all. That is the type of thought that drives development. If everything was "good enough" scientific and mathematical modeling would just stagnate, no string theory, quantum mechanics, etc...
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Originally posted by joe shmoI would say that is the kind of thought that leads to spending hundreds of millions
"And I don't see why we need anything more complex than that."
I didn't say we "need" a different way to do it. I just asked if there "is" a different way to do it. I (and I think most others) would prefer to have the machinery and not use it, than not have it at all. That is the type of thought that drives development. If everything was "good enough ...[text shortened]... tific and mathematical modeling would just stagnate, no string theory, quantum mechanics, etc...
developing a pen to work in space instead of just using a Biro.
I don't believe that there is a simpler way of doing it than comparing the two slipping
points and seeing which is smaller.
There are of course an infinite number of more complicated ways of doing it.
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Originally posted by googlefudgeI wasn't really concerned with it being simpler solution(for this particular problem), just more complete in general. I just assumed that since it wasn't "put in some parameters, turn the crank, and out comes the result" machinery that is more typical of garden variety mechanics, that somebody had classified it, and/or researched the problem variety in detail.
I would say that is the kind of thought that leads to spending hundreds of millions
developing a pen to work in space instead of just using a Biro.
I don't believe that there is a simpler way of doing it than comparing the two slipping
points and seeing which is smaller.
There are of course an infinite number of more complicated ways of doing it.
If I was wrong, no big deal... Just looking for some conversation on the subject.
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Originally posted by apathistPersonally...I think this almost certainly "is" a simulated reality. There is no way I can figure that the whole of existence can be logically real. Try to logically find a way to "get outside". This paradox is has been know since man could ponder existence. Nested Dolls, Turtles on turtles, etc... Try to put yourself in a "robots shoes" and ask yourself the following questions: If I we do actually exist, how do we ultimately exist in nothing?
If I understand your question. Because the other option is that we are in a virtual reality. I guess that's possible. But I am not a pixel. Am I? Now I'm all angst-ridden.
How does nothing ultimately exist, if we actually exist?
I think our "existence" is just the axiom of choice.
Originally posted by joe shmoI'm experienced about the ubur-verse. What level are we attacking here? We may be a dream, but then what about the dreamer?
Personally...I think this almost certainly "is" a simulated reality. There is no way I can figure that the whole of existence can be logically real. Try to logically find a way to "get outside". This paradox is has been know since man could ponder existence. Nested Dolls, Turtles on turtles, etc... Try to put yourself in a "robots shoes" and ask yourself ...[text shortened]... ultimately exist, if we actually exist?
I think our "existence" is just the axiom of choice.