Gravity observed with Cavendish setup

DavidB66

Active Member
This looks a lot better designed than most non-academic attempts at Cavendish experiments. (I won't mention some of the worst!) I like the way the equipment is shielded from air currents.
Still, a few doubts occurred to me:
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? Most people find it impossible to avoid some initial rotation, which takes hours to damp down. I once tried a (very crude) experiment myself, and gave up after a few hours, as patience is not my strong point.
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.
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?
 

Jesse3959

Member
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!
 
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Jesse3959

Member
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?
I had a few more thoughts on this.

Taking yet another approach, looking later in the video, it seems to be oscillating around the big weights with a period of about 1302 seconds, very roughly.

Using this pendulum calculator: https://www.omnicalculator.com/physics/simple-pendulum

My pendulum length (Half of my beam) is about 10cm.

The calculator says an acceleration of 0.00000232883 m/s^2

In this position, the distance between the centers of the two lead weights is about 5cm.

This would give a force (if they were spheres) of 1.02770283e-7 Newtons, which would give an acceleration on 0.6861kg
of: 1.4978907302143E-7 m/s^2.
The pendulum calc says: 2.32883E-6 m/s^2

So that's a touch more than an order of a magnitude off -- but the oscilations were very small and it was hard to tell exactly where one cycle started and the other ended.

And I also may have got lost in the math ha ha!
 

DavidB66

Active Member
Wow, that's a lot of work!
I'm afraid I don't understand the math. What do the letters 'e' stand for? 'e' usually stands for Euler's number, but I don't see how that comes into it.
Cavendish himself estimated the gravitational attraction of his weights, at the appropriate distances, as not more than 1/50,000,000 that of the earth's gravity. I did a rough calculation assuming the relevant mass is 10 kg and the relevant distance 10 cm, and got a result of about 1.7 x 1/100,000,000, which is in the same ball park as Cavendish. This implies a very, very small acceleration compared with that of earth gravity, which is about 10 m/sec^2. If we were generous and took the ratio as high as 1/10,000,000, the acceleration in millimetres per sec^2 would be 10,000/10,000,000 = 1/1000, so assuming constant acceleration (which seems reasonable until the weights have moved significantly closer together) it would take about 20 minutes for the velocity to reach 1 mm per sec. But of course, once it gets to that rate, it takes less than 10 more seconds to cover 1 cm! (I'm assuming effectively zero resistance from the string, etc.)
Unless I have made some horrible blunder (which is entirely possible), the total movement observed is not obviously impossible, but I'm still not sure about the acceleration observed. After the large weights are moved, the test weights seem to respond visibly within about 10 seconds, which seems rather quick. [Correction: I had forgotten the x60 speeding up of the video! But even allowing for that, the response is still surprisingly quick.]
 
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Jesse3959

Member
Oh sorry David, e stands for exponent I guess.

e-7 is the same as *10^-7.

Google calc and most online calculator applets support using e to mean *10^whatever.
The weights never ever reached 1mm/second.

And many of them even return values like that.

The copper tube is about 9mm from side to side, looking at the end. So you can watch the end and see how long (according to the top-left timestamp) it takes it to move one tube's width by holding your mouse on the screen at the leading edge of the tube, playing the video with the space bar, then pausing it when the other edge of the end of the tube is where the mouse is. Pause again with space bar.

I measured about 9mm in 153 seconds, or about 0.06mm/second.

Does that seem better to you?

As to the test weights responding in 10 seconds, I'm assuming you mean realtime - in other words, 10 frames. I just looked (You can pause a youtube video and move forward and back one frame at a time with the , and . (or < and > ) keys.

I don't see any perceptible move in the first 10 seconds according to the time stamp in top left of the picture.


I do see it move a tiny bit by the time 30 seconds has elapsed.

If you mean 10 minutes, the displacement calculator says it should move 1cm in the first 10 minutes of freefall. It moved like 3cm in the first ten minutes.

But anyway, this is why I'm planning to build a better setup that's designed to accurately measure. At least more accurately than this ha ha!
 

DavidB66

Active Member
...

The copper tube is about 9mm from side to side, looking at the end. So you can watch the end and see how long (according to the top-left timestamp) it takes it to move one tube's width by holding your mouse on the screen at the leading edge of the tube, playing the video with the space bar, then pausing it when the other edge of the end of the tube is where the mouse is. Pause again with space bar.

I measured about 9mm in 153 seconds, or about 0.06mm/second.

Does that seem better to you?

As to the test weights responding in 10 seconds, I'm assuming you mean realtime - in other words, 10 frames. I just looked (You can pause a youtube video and move forward and back one frame at a time with the , and . (or < and > ) keys.

I don't see any perceptible move in the first 10 seconds according to the time stamp in top left of the picture.


I do see it move a tiny bit by the time 30 seconds has elapsed.

If you mean 10 minutes, the displacement calculator says it should move 1cm in the first 10 minutes of freefall. It moved like 3cm in the first ten minutes.

...

Thanks again, Jesse.

I think our calculations are in the same ball park, and after allowing for the time lapse effect, I don't see any obvious reason to reject the observations. I'm sorry if I seemed pernickety, but there are some very overconfident 'demonstrations' of Cavendish on YouTube, and it's important to check the results. I recall that the excellent 'Miles Davis' got some positive initial results when he tried it in 2018, but had second thoughts. Reading through the comments on his original video again reminds me that Walter Bislin has a 'Cavendish simulator' to show what should be expected with various choices of parameters:

http://walter.bislins.ch/bloge/index.asp?page=Cavendish+Experiment+Simulator
 

Jesse3959

Member
E-7 = 10^-7

e-7 = - 4.28172

Capitalisation is important here, a capital "E" is the exponential function but a lower case "e" represents eulers number (2.71828) as @DavidB66 notes.
Thanks my friend, but it's not as universal as you think.
A lot of people use a lower case e for exponent - right or wrong, and I realize e is also a constant. But that's the way it is.

For example, in the python version 2.7.11programming language, it prints out exponents like this:
>>> 0.00000000123
1.23e-09

And the programming language Perl v5.22.2 prints it out like:
print 0.00000000000000000000123;
1.23e-21

gcc version 5.3.0 let's you choose between e or E for exponents, but people often use e, see here:
https://stackoverflow.com/questions...mber-of-exponent-digits-after-e-in-c-printf-e

And believe it or not, if you go to google.com and search for 1/100000000000000 it will calculate it for you and tell you it is 1e-14 with a lower case e.

Now granted, there are lots of people that use E as well.

But anybody who's been around numbers at all in the real world would have to realize that both e and E are (rightly or wrongly) used interchangeably, and besides, it should be at least a little obvious when we're talking about very very small forces of such an experiment that a figure like 1.02770283e-7 would *have* to be a really small number :D

But thanks anyway.

EDIT: PS: The reason I mention Perl, Python, GCC, and Google is because there are millions or billions of people using these tools combined - and if lower case e as an exponent was taboo there'd be a huge outcry. But I'm sure there are a very very small percentage of people who are on a mission to rid the world of lower case e usage as exponent, just like there are small groups of people fighting against about any single thing you can think of :D
 
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Jesse3959

Member
Thanks again, Jesse.

I think our calculations are in the same ball park, and after allowing for the time lapse effect, I don't see any obvious reason to reject the observations. I'm sorry if I seemed pernickety, but there are some very overconfident 'demonstrations' of Cavendish on YouTube, and it's important to check the results. I recall that the excellent 'Miles Davis' got some positive initial results when he tried it in 2018, but had second thoughts. Reading through the comments on his original video again reminds me that Walter Bislin has a 'Cavendish simulator' to show what should be expected with various choices of parameters:

http://walter.bislins.ch/bloge/index.asp?page=Cavendish+Experiment+Simulator
Thanks David!

I really appreciate the pernickety! I'm fully aware I may have overlooked something! And I agree, there are some very overconfident demonstrations!

In fact I know the feeling myself. When I started out I had a longer beam with pints of water hanging, and it was in the open air. I found when I stood near it, the weights began visibly moving towards myself. I was elated until I realized it was moving too fast and it wouldn't move towards other heavy weights. Then I realized the warmth of my body was causing an updraft which was sucking the weights towards me ha ha ha!

I really appreciate it when someone takes the time (as you did!) to help me look for mistakes I may have made!

And thanks for the link!
 
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