Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: dedaNoe on 07/04/2007 10:07:18
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this is newton's gravity:
FR2=γM1M2
coulomb's law is formally same:
FR2=-kQ1Q2
if X is either charge or mass the leverlaw is:
F1/F2=X1/X2=D2/D1
1+F1/F2=D2/D1+1
(F1+F2)/F2=(D1+D2)/D1
(F1+F2)/(D1+D2)=F1/D2=F2/D1
F1F2=D1D2Sqr((F1+F2)/(D1+D2))
F1/X1=F2/X2=G
F1F2=X1X2G2
F1/D2=F2/D1=GSqrt((X1/D1)(X2/D2))
the leverlaw is true gravity law and law for electromagnetic interaction.
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while i am here:
consider the system earth - moon. take any weight and move it along the line that connects their centers. you'll come to a point where the pull of the two on the third weight cancel. that's newtonian barycenter - equivalent to leverian equilibrium point. from the barycenter to earth is D_e and from the barycenter to moon is D_m. with newton's gravity and action = - reaction we get F_e=GM_eM_test/D_e^2=-GM_mM_test/D_m^2=-F_m which simplified returns M_e/M_m=-D_e^2/D_m^2. that would be newton's condition for balance in the system: the weights must be proportional to the squares of their distances from the center. now consider the earth - moon system as lever. the leverlaw says: magnitudes are in balance on distances that reciprocate thier weights. in the system we review the equation for balance would simply be F_eD_e=F_mD_m or M_eD_e=M_mD_m. how can this two conditions for balance be both right at the same time?
i'd like to put accent on the fact that archimedes' leverlaw - magnitudes are in balance on distances that reciprocate their weights - has no exceptional case, mentions no rigid bar and no fulcrum, doesn't even mention the lever its self. so when do we apply the leverlaw, a? from the content of the leverlaw we can simply define lever as system of weights (as bodies) where every weight is global representor to its own lever. weight as body is ordered array (vector) of all the potential equilibrium distances i.e. forces and actual equilibrium distances - potentially negative forces.
someone stop me... i always get carried away when talking levers. it's simply cause i have so much to say. check my nukebook http://dedanoe.googlepages.com/knigata.pdf in case you juddge the book by its cover click here http://dedanoe.googlepages.com/korica.jpg
dedanoe over and out...
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By 'leverlaw', are you referring to the principle of moments?
This refers to the 'turning effect' on a rigid body (which implies a lever; all parts of the object are linked, rigidly, to each other).
The moment of a force is Force X Perpendicular Distance from a reference point, which doesn't have to be a pivot, as you say. A body will experience no turning effect if moments about this point add up to zero.
The Earth and Moon are not part of a rigid body/system so you can't really apply moments.
Gravitational attraction is proportional to Mass1 X Mass2/dsquared. (I am assuming point masses at the centres of mass of each body, but that is ok for my purposes). At a Lagrange point, in space, the two weight forces are balanced
The term 'balance' refers to different things for each of the two situations which I think you are describing. One situation has equal and opposite moments ('equilibrium' in my textbooks) and the other has equal and opposite ('balanced') forces.
There is no conflict.
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there is no such rotational moment (torque) measured in newton meters cause the force and distance can be collinear too and still the lever will be functional. what you don't know is my dynamic leverlaw:
NewForce = ExtremeForce * Cos(a) - ExtremeDistance * Sin(a)
NewDistance = ExtremeForce * Sin(a) + ExtremeDistance * Cos(a)
pick the ExtremeForce and the ExtremeDistance as vectors and roll "a" form -pi to pi. "a" is the phase of the harmonic oscillation.
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Do you have another reference to your 'leverlaw"?
I have not come across it before. Is it your own or does it exist in published literature?
Possibly, something is lost in translation?