Mike-from-the-Bronx

forum.txt

How about something low tech like this: The switch is hidden behind a loose brick. During the day the loose brick is indistinguishable from all the other bricks that make up the building. But at night, because the interior of the building is well lit, a sliver of light shines through a crack above the brick. The protagonist would see the light, pull out the loose brick, flip the switch, replace the brick and toss some loose dirt into the crack so the bad guys would not see and follow.

I took a stab at this with my simulation program. I copied the arrangement offered by Edwina Lee. The arrangement implies a parent/child hierarchy as suggested by Bluemoon. In my simulation, the user does not declare the order of processing. The hierararchy defines it. Parent first, then child, grandchild, etc. Here's a link to a video I created from the results. http://www.relativitysimulation.com/Documents/Nested_Bowls.mp4

Oh. Then I with draw my criticism.

Oh boy. I just realized something embarrassing. When analyzing the contributions of the pans it is important to define the hanging point of the pans to be at the same elevation as the pivot point. Otherwise there will be non-offsetting torques contributed by the pans. I just added that caveat in my document.

Draw a free body diagram of the balance beam. Place a mark at the Center of Mass. Place another mark at the Pivot Point. Draw a vertical arrow through the center of mass. That’s the “f” in the formula, the force of gravity. Draw another arrow from the pivot point to the center of mass. That’s the displacement (the “r” in the formula) Torque is the cross product of those 2 arrows (vectors). That’s all there is to it. (I have done so many of these kinds of analyses it is instinctive. But to someone who only saw this kind of thing in an introductory physics class I imagine it could get confusing.)

Fair enough. I can't seem to post images here so I will try to post a link to an MS Word document with images. Hope this works. http://www.relativitysimulation.com/Documents/balancebeam3.docx

I accidentally voted this post up when I wanted to vote J.C.MacSwell up. swansont, you have displayed a lot of understanding in a lot of posts, but in this one you are dead wrong. J.C.MacSwell is dead right. Try re-posting this discussion on a classical physics or mechanical engineering forum and you will quickly be told that.

That works for me.

Post #18 is again very confusing. But the last statement (question) is valid. No analysis has yet been presented to show that a restoring torque exists on a balance beam which has been displaced from its normal horizontal position. I can't find one.

Good job studiot. (and your assessment of TakenItSeriously is spot on too)

If I understand you correctly, your conclusion would be that a Square moving at a 45 degree angle would just be a smaller square. Relativistic contraction does not work that way. (Edit: added "When....")When transforming reference frames in relativity velocities don't combine by the rules of vectors and neither does contraction. Example: If you take an object that is initially a square at rest with respect to you and transform to a reference frame that is moving northwest, the northwest and southeast corners of the square are contracted (closer to the center). The northeast and southwest corners are not effected at all. Connect the corners to determine the shape and it will be a symmetric diamond.

I am satisfied that the analysis I provided in my link in post #23 is correct and consistent with SR. But nobody’s perfect and I’ll try to stay open to the possibility that I made a mistake. I’ll be glad to go over the analysis step by step with anyone who wants. But I would ask that the requester first demonstrate their level of proficiency in SR by at least trying to solve the following 2 step problem. Given a 2D shape that is a square with proper dimensions 2 light-sec on each side when at rest with respect to reference frame S. One set of space time coordinates (common time for the 4 corners) with respect to S are; Corner a: (t, x, y) = (0, +1, +1) Corner b: (t, x, y) = (0, -1, -1) Corner c: (t, x, y) = (0, +1, -1) Corner d: (t, x, y) = (0, -1, +1) Where t is in seconds and x and y are in light seconds. Given also that there are 2 other reference frames S’ and S’’. S’ has velocity (vx, vy) = (-.6c, 0) with respect to S. S’’ has velocity (vx, vy) = (-.6c, .6c) with respect to S. Transform the shape to S’. Provide the velocity of the shape with respect to S’ and one set of space time coordinates with common time for the 4 corners. Transform the shape from S’ to S’’. Provide the velocity of the shape with respect to S’’ and one set of space time coordinates with common time for the 4 corners. Note: Task 2 is not a request to transform from S to S’’. I is a request to transform from S’ to S’’.

Well, I would not take that approach. I spent some time doing the full calculations. Link below. Interestingly, there was no rotation as I had previously predicted. I know the rotation shows up sometimes but, apparently, not for this problem. If you browse the document you will see that it is not entry level stuff. http://www.relativitysimulation.com/Documents/Square%20in%20Rectangle.htm Added this comment: I hope I copied all the numbers correctly.

I appreciate the suggestion, but Lord No. I stay away from visual effects in SR. I understand the existence of such effects but dealing with them is beyond me. I was referring to the following phenomena in SR: 1. Start in an inertial reference frame for which an object is at rest. Note the proper dimensions and (proper) shape of the object as given by the coordinates. 2. Sequentially perform multiple transformations to other inertial reference frames with different relative velocities in 2D or 3D space. 3. Transform back to a reference frame for which the object is at rest. Note the proper dimensions and (proper) shape of the object as given by the final coordinates. My experience (from doing shape transformations by the thousands) is that the final coordinates will define the original proper shape except that the shape will be rotated by some amount that is a function of the combined transformations. This SR behavior has been documented but I don't have a reference or name for it right now. studiot, in post above, suggested Thomas Precession. P.S. For any laymen reading this, note that transforming a shape, like a square, in SR is not as straightforward as just applying the Lorentz Transformation to the 4 corners. The LT will give you 4 coordinates in space for 4 different times. Relativity of Simultaneity. To determine the shape in the new reference frame, you have to adjust the spacial coordinates for one common time. If you are going to perform all 3 steps, you also have to calculate the relative velocity of the object with respect to each reference frame so that you know how to get back to zero relative velocity at the end.