INTRIGUING MECHANICAL PROPERTIES by Nathan Coppedge ABOVE: Single-Module Unit, Side View ABOVE: Single-Module Unit, View of Counterweight and Pivot ABOVE: View of advantage of smaller ball. ABOVE: View of advantage of larger ball. ABOVE: View of small ball after natural outwards motion. INTRODUCTION Since my discovery of some interesting mechanical properties, specifically natural torque, in Fall 2000 (I was 17 years old and that is not the subject of this particular discussion), I have gradually since 2009 engaged in experiments designed to prove that physics includes some very clever mechanics. Although I designed many different simple machines in order to demonstrate unusual mechanics, one in particular stands out, as it is the subject of my 2-Part Evidence. It takes the form of a Single-Module involving a counterweighted lever which passes through an upward-sloped track so as to act on a ball. Upon the return, an almost-matching downwards slope is introduced, permitting return of the ball to a very similar location. Recently I have endeavored to prove that with a larger ball following similar weight and leverage ratios as below (the subject of a dream about a lemniscate), the device expresses the properties of what might be called a perpetual motion machine. Keep in mind that given the ratios, the natural back-and forth movement is a proven principle that I have shown in countless videos. To reset the cycle is a more difficult problem that is the subject of this paper. Due to the proven natural motion and upwards-and-downwards orientation of the track, transitions between tracks are not likely to be a problem in themselves assuming the barrier to cyclicality can be overcome. Details: Lever Attributes: 9.5X - 11X : <6X measured in units from the fulcrum at estimated center of mass, in other words, a long-end leverage ratio of about 1.58X to 1.83X. Counterweight Mass not including balance structure: 41.546 grams (see notes below on calculation). Effective long-end leverage mass without counterweight = 35.18 effective leverage expressed in (grams * leverage), or significantly less than counterweight. Steel Ball Mass: 28.246 grams (¾ inch chrome steel G25) Angle of Lever: about 4 - 9 degrees, downwards-sloped. Track angle: About 1 - 2 degrees upwards-sloped, < 1 degree downward-sloped on return. ADDITIONAL SUPPORT: It is suggested since the lever is mobile and upward motion of the ball has been proven to take place when the ball is supported (simply analyze the ratios using a conservative version of the ½ m * d rule) then what is necessary to continue motion is two things: (1) A higher altitude upon return than the desired location of return permitting ‘room to move into’, and (2) A significant angular advantage upon return in the height of the mass applying weight, in other words, in this case, a mass-leverage advantage as expressed in applicable mass and leverage. Interestingly, in spite of the fact that the ball loses altitude relative to the lever, conditions (1) and (2) can still be met. (1) Since the ball gains altitude along the first portion of the track, and the slope of the first portion of the track is at least 1 degree upwards-sloped, the return track is permitted to gain altitude against the original track, as it is well known that motion often takes place with a downwards-sloped angularity of less than 1 degree, after all the lever is mobile and in principle the lower altitude can be acquired particularly with a lever advantage, and (2) The height of the ball is not constrained by the appropriate weight and leverage ratios, instead practically any size can be used assuming the leverage ratios and mass ratios remain the same. Note that the masses are flexible so long as the leverage ratios are maintained---not the leverage in real units, but the leverage ratio. This means the ball can be practically any scale or mass relative to the track, and still meet requirements. Therefore, the ball is permitted in some cases to have a height advantage which places the midpoint of mass well above the highest relevant point of the lever upon return, which means that the ball can apply very close to its full mass--given that the change in height has not been very extreme, and the height advantage exists. Therefore, given that room to move into is a virtual possibility, all of the criteria for resetting the cycle have been met, given that natural motion takes place at every other point, and that transition is easy at the end of the module due to the downwards return [See images]. Also note, that the motion that takes place occurs naturally as there has been zero inputted kinetic energy except as expressed in altitude of mass. This has been proven again and again in this and similar arrangements. Therefore, there appears to be no remaining barrier to the concept of un-powered repeating natural momentum from rest with no net altitude loss, which is called perpetual motion. VIDEO DEMONSTRATION: The 2-Part Evidence is Viewable Here: [ https://www.youtube.com/watch?v=gUSQCy5nxY4&list=PLcttXCrYoAgP88CiJ3ibPqVl1FjlAAIdi ] If you would allow an online edition, I have several other videos which may be worth including, one of them showing natural two-directional motion: [ https://www.youtube.com/watch?v=RgE_xLqIbkw&list=PLcttXCrYoAgP88CiJ3ibPqVl1FjlAAIdi&index=2 ] The general list of all experiments may be found here: [ https://www.youtube.com/playlist?list=PLcttXCrYoAgP88CiJ3ibPqVl1FjlAAIdi ] NOTES ON WEIGHT RATIOS (3 US quarters, 8 US pennies, and 2 US dimes, and 5 inches of duct tape). 1 U.S. Quarter = 5.670 grams, X3 = 17.01 grams 1 U.S. penny = 2.5 grams, X8 = 20 grams 1 U.S. dime = 2.268 grams, X2 = 4.536 grams == 41.546 grams Ball weight: 28.246 grams (¾ inch chrome steel G25) Coppedge, Nathan / Undergraduate Student 2018/06/23, p.