a) there doesn't seem to be much rotation of the test weights around the 'string' before the large weights are moved. Did you have to wait a very long time before the apparatus settled down?
I had to let the suspended beam settle for a bloody long time! That was the most frustrating aspect of the whole thing. I worked on the project for weeks as I recall, gradually improving it bit by bit. But yes, I'd set it up then go to work or go to bed, then come back and see if it had settled yet. And if the temperature in the house changed, then the neutral twist state of the monofilament nylon fishing line would change, and it'd need to settle again...
b) when the large weights are moved, this will create some air currents inside the box, which could affect the test weights. But you have provided some control against this by moving the large weights round in opposite directions and still getting the same results.
Good thought, and in fact some flat earther's have told me that the water in the tuna can got to spinning and was turning the whole balance beam that way (because the balance beam has a brass wire sticking off the bottom into the water to keep static differentials down.)
But remember, the video is playing at 60x speed. So what takes 10 seconds to watch took 10 minutes to record.
And it takes the weight sometimes 10 seconds (10 minutes realtime) to accelerate to full speed - which would mean the air (or water) would have to be spinning *faster* for the full 10 minutes. And the water in the tuna can and the air in the box is *not* going to be spinning very fast for very long.
Furthermore, it's physically impossible for that to account for it because when the fixed weights are rotated, the air cannot be spinning the same speed. It'll be spinning maybe a hundredth of that speed. And the suspended weights would be limited to a fraction of the air speed. So it's physically impossible for the hanging weights move the same distance as the big weights - there is always loss in a viscous drive.
But in my case, the hanging weights essentially followed the big weights exactly degree for degree without any slippage loss.
And if it was just the water (or the air) spinning, it'd continue to spin the suspended weights, not cause them to overshoot and then rebound back the other way to be nearer the big weights.
c) the response from the test weights is surprisingly quick. The gravitational attraction of a few kgs of mass is so small that even without any resistance in the string it should take quite a while for any movement to be noticeable. Have you worked out what the theory predicts to compare with the results?
That's a good question. I remember doing a rough calculation last year and I remember it being within an order of a magnitude roughly, but I don't remember the specifics.
So here's the basic info:
Small weights:
0.6861kg each, including the screws, and the portion of 3/8" OD copper tube near the weights.
About 3cm thick at the top (Wedge shaped, tapered towards the bottom.)
Large weights: 5.610kg
About 10cm wide, 5cm thick.
I weight each pair of weights together and divided by two, so it's average.
Unfortunately the camera angle makes it very difficult to get exact distances, but knowing the dimensions of the lead blocks we can maybe sort of guesstimate at how far the weights are moving. I wish I'd set it up with a graduated scale and a pointer, but frankly I started out not knowing if I could even get any apparent attraction at all. My whole mindset was "See if I can prove an attraction." Actually measuring it wasn't part of the mindset till the very end when I was just about done.
Looking at the frames, it looks like the acceleration took 329 seconds to go the first centimeter of "Freefall" towards the big weights.
I just set up the blocks to recreate the view from the video at time stamp (top left corner time stamp) 9:28:35 and I measured 8cm between the centers of the weights. I take that to be the average distance during that first centimeter of acceleration. (I know this is all real rough measurements. But that's really all we have for options right now. Lord willing I'll be doing a much better one later this year and set it up to carefully measure it.)
Now mind you, I'm no math wiz. So I'm sort of grabbing at straws for the following math. Hopefully a math wiz can drift by and take my raw measurements and come up with a calculation! But in the mean time, I'll do my best. Which I know is shoddy.
I do know that the force would be G * ((m1 * m2) / dist^2) - or 6.6743e-11 * (((0.686136126531*5.610370625) / (0.08^2)) = 4.014e-8 Newton
Using this online calculator:
https://www.omnicalculator.com/physics/impulse-and-momentum
Giving it the above force in newtons and mass of the small weight and a time of 329 seconds, it says it's velocity would be 0.000019248 meters per second. That's 0.6332592 cm in 329 seconds. That's awfully close to the 1cm it looked like it moved in those 329 seconds.
(But remember, that was the final velocity, not the average velocity since it started at 0..)
I realize this is an approximation, but I'm doing the best I can here.
Taking another approach, using this calculator:
http://www.endmemo.com/physics/force.php to convert force and mass into acceleration, we get 5.8504591167468E-8 m/s^2.
Then using this displacement calculator:
https://www.calculatorsoup.com/calculators/physics/displacement_v_a_t.php
This gives a displacement of 0.315cm - which is quite a bit below 1cm.
Anyway, considering the numerous sources of error (like the fish eye odd viewing angle of the camera, etc) and the fish line and everything, it seems surprisingly close. Within an order of a magnitude.
The lead blocks also weren't spheres. They were 2x4x4" lead bricks. So the near part of the big weight was much more near than it would have been for a sphere, which would have sped it up possibly.
Anyway, in answer to your question, it does appear to be going faster than it should (at least for spheres and with no interaction of the fish line/etc) but it's only about 3 times too fast. And from the difficulty of measuring G, I guess I'm satisfied that it's ball park enough to allow me to suspect G was a significant factor.
Taking another approach:
Using this calculator:
https://www.omnicalculator.com/physics/free-fall
it says the "Freefall" for the first cm should have taken 1060 seconds. Which again is 3 times what I measured.
Anyway, I'm planning a new setup with nearly 16 foot long beam made of carbon fiber fishing rods, using glass spheres as weights (and maybe bags of glass marbles for the big weights?) and I plan to not have the rotating tuna can of water. And instead of the fish line I'm hoping to use sapphire watch pendulum pivot bearings. Not sure if that'll work but I really want to get rid of the variable torsion aspect of the fish line. Waiting for that to unwind and settle was miserable.
Furthermore, I'm planning to mount the camera so it has a better view, and install a graduated scale in centimeters with a pointer on the moving arm so the exact displacement can be accurately measured in the video.
But there's a lot of speculation if the watch bearings will work. But they are "in the mail."
Hope this helps!