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  1.  
    By adding up the masses like that you seem to be ignoring the pulleys, which serve to effectively flip the sign of the end masses with respect to the beam - and we are only interested in calculating with respect to the beam. I think.

    The actual physical model I have in mind here is a magnetic field whose gradient of interest here lies along the beam direction. There are two current loops lying in the horizontal plane, such that where they are closest their currents add. Now applying the motor rule F = B I L gets you to this mechanical analogue.
    •  
      CommentAuthorAngus
    • CommentTimeMar 4th 2014
     
    Posted By: Andrew PalfreymanBy adding up the masses like that you seem to be ignoring the pulleys, which serve to effectively flip the sign of the end masses with respect to the beam - and we are only interested in calculating with respect to the beam. I think.


    Not at all. The masses do not have a sign. As long as the strings are in tension they may as well be located where the strings are connected. If the strings are not in tension, you are violating the First Principle of Engineering.

    The forces of course do have a direction, and I have accounted for it properly.
    •  
      CommentAuthoralsetalokin
    • CommentTimeMar 4th 2014 edited
     
    Leave the strings outside around here lately, and you'll soon be able to push them, since they will first be wet and then they will be frozen stiff.

    I still don't see how you get a torque out of it. Choose any point on the beam as the origin, say the left end. The string pulling up on the left end has no moment arm so produces no torque. At L/2 you have force +2 downward, and at L (the rightmost end and suspension point) you have force +1 directed upward. The two moments cancel perfectly and the damn thing just sits there.

    And don't complain that the beam's mass creates a non-cancelled torque around the reference point, because you stipulated that the mass of the beam may be neglected. If it cannot, then you are constrained by reality and you must compute your moments about the true center of mass, center of gyration, centroid, whatever you wanna call it.
  2.  
    OK, I can see that this simplification is actually worse than describing the actual thought experiment. A magnetic field lies along the beam direction. Firmly attached to the beam are two side by side current loops (superconducting). Where they abut, currents run in the same direction. This is a space experiment, so there is no gravity. But since there are forces, we'll assign a mass M to the beam and its current loops. It helps thinking to have the current loops rectangular. The sides, running parallel as they do to the field, contribute nothing to the forces.

    Recall that a single current loop in a uniform magnetic field seeks its lowest energy configuration by aligning itself so its own magnetic field lies along the B direction and is in phase with it. A compass. But here I'm using two loops that want to do the opposite thing, yet are mechanically attached to one another (that's the only purpose of the beam - as a mechanical support)

    If the field B is uniform over the beam's extent, then there is no net force, and no net torque. I am considering the case where the field gradient dB/dx is nonzero (x being the beam direction).

    Now we can all forget about pulleys and bent strings and the like
  3.  
    Are you trying to build a Schleppian drive, a Poynting vectorator? Those aren't scheduled until sometime after 2075.
  4.  
    My bad. I'm cheating the timeline.
  5.  
    Posted By: alsetalokinI still don't see how you get a torque out of it.
    If d=0, there is no torque. Else (see my previous post) the torques are -3d, -2d and -d at LHS, middle and RHS resp.
  6.  
    Posted By: Andrew Palfreyman
    Posted By: alsetalokinI still don't see how you get a torque out of it.
    If d=0, there is no torque. Else (see my previous post) the torques are -3d, -2d and -d at LHS, middle and RHS resp.

    Yes, and in that case you get the wrong answer because now you must use the center of mass of the coupled moving parts as the reference and compute your moment arms from there.

    After all, your answer says the thing will rotate one direction. Walk around to the other side of the beam and do the problem again.
  7.  
    Planoforming drive. That's what it is.
  8.  
    Insofar as my ability to add and multiply survives, my answer is correct.
  9.  
    The force on a current-carrying element of length L carrying a current I laying at right angles to a magnetic field B produces a force F = B*I*L in a direction at right angles to both the field direction and the current direction. But y'all knew that.

    The question to which I seek an answer is this: how much net lift can be obtained by exploiting the changes in magnetic field on or near to the surface of the Earth? Some stakes in the ground:
    Jmax = 5*109 A/m2 (YBCO tape, critical current density)
    dB/dx|max = 6*10-12 T/m (around here, fortuitously)

    Issues:
    1. dB/dy is the critical value: dB/dx can only produce a torque.
    2. At first blush, the maximum mass density allowed is exceeded by all known materials
    3. Is there a geometry that suppresses torque while leaving delta-Force intact?
    4. Is it the case that this might work at least at the magnetic poles?

    I'm going to get off this fucking rock even if it kills me!
    (and No, Trim, you may not load me into a railgun)
    •  
      CommentAuthorAngus
    • CommentTimeMar 5th 2014
     
    The force on a current-carrying element of length L carrying a current I laying at right angles to a magnetic field B


    lying.
  10.  
    So when you are wrapping the windings onto the armature, is that called "lying up" or "laying up" the wire?

    That jumping shot right near the backboard is properly called a "lie-up" instead of a lay-up?

    Instead of layyers we need lie-yers?
    •  
      CommentAuthorAngus
    • CommentTimeMar 5th 2014 edited
     
    (1) laying up. Transitive use of the verb

    (2) lay-up. Jargon. Nothing to do with regular grammar. I await the judgement of the entomologists or whatever they call themselves.

    (3) Wretched pun related to a different verb.Wasting my valuable time here.
  11.  
    All verbs should be used transitively. Otherwise they just lay there, doing nothing.
    • CommentAuthortinker
    • CommentTimeMar 5th 2014 edited
     
    Like giant Iceverbs, drifting in the word-dark see-a.
    • CommentAuthorloreman
    • CommentTimeMar 5th 2014
     
    Posted By: tinkerLike giant Iceverbs, drifting in the word-dark see-a.


    That's very poetic Tinker. I think I'll pinch it.
  12.  
    Iceverbs are mostly subsurface. Nouncicles, on the other hand, can kill.
  13.  
    eschatologists
  14.  
    The question to which I seek an answer is this: how much net lift can be obtained by exploiting the changes in magnetic field on or near to the surface of the Earth?