How Can a Table Float with Buckets?

[Chandra Prayaga]

Hello Physics Forums, Deployment here. After browsing the internet I came across this photo..

I have been pondering and pondering on how this is actually possible. If you think about it, the buckets are actually holding down the table.

Does anybody have any idea how you would conduct calculations on doing this?

Thanks,
- Deployment​

Analyze each object separately. The forces on each bucket are: Weight of the bucket, tension in the rope, and the normal force from the table. These should add to zero.
The forces on the table are: The weight of the table, the normal force by each bucket down on the table (this is what you meant by "buckets are actually holding down the table", The vertical component of the tension in each string tied near the center of the table. These should add to zero. By symmetry the horizontal components of the tensions in the strings tied to the table will add to zero.
Write down these two equations, and you will find that with the given data, you can solve for everything.
The equation for the torques does not add anything. The symmetry of the arrangement guarantees that the torques will add to zero.

 

[Tyler Worden]

Deployment has the answer.

Weigh the table, divide it in 4, calculate the weight needed to equalize ¼ of the table weight using the string angle. Make sure the string angle is enough to position the table above the floor. Lift the table above your calculated height, add your necessary weight to the buckets then allow the table to lower and suspend at it’s equalized weight height.

By the way, a bosun's chair needs 2 men and a boy lifting, when anyone is sitting in it; you need to lift the weight of the chair as well as the person in it... Or! Normally you pull it up empty, tie it off then climb up and sit in it.

 

[sophiecentaur]

By the way, a bosun's chair needs 2 men and a boy lifting, when anyone is sitting in it; you need to lift the weight of the chair as well as the person in it... Or! Normally you pull it up empty, tie it off then climb up and sit in it.

HaHa. You have my sympathy there, and you are welcome to try to climb the mast on my boat, unaided and without mast steps.
But your comment demonstrates the vast difference between Mechanical Advantage and Velocity Ratio (=Efficiency), which is a point that only I seem to make, ever, on PF. The VR of a self-pulled bosun's chair is 2 and the MA is something less than 0.5 (assuming you can normally lift your own weight yet you need another person's help). So the efficiency is MA/VR = <25% ! Bosun's 'chairs' are normally canvas and webbing and will be no more than a couple of kg so the losses must be due to friction in the (usually pretty expensive) halyard pulleys and compression in the rope as it goes over. But I guess the pulleys are not designed to turn efficiently under a 100kg (1kN) load. I'd bet that a really good pulley (also large diameter) at the top would make things a lot easier - but who would think about that when their mast happens to be laying down in the yard?

 

[arydberg]

This is simple. The weight of the table is equal to that of the buckets. A little push and you could make the buckets float 1 inch above the table. It would still be a static system and would not move.

1) First think about 1/4 of the table and 1 bucket. Then replace the bucket by 4 pounds of weight. Then replace the weight of the 1/4 table by another weight of 4 pounds. It will be a static system because the two weights are equal. If the weights are not equal things will move.

2) for the second step suspend 2 separate 4 pound weights over a table. As the string angle increases the weight of the table must be decreased to keep a constant tension in the string.

 

[arydberg]

Deployment has the answer.

Weigh the table, divide it in 4, calculate the weight needed to equalize ¼ of the table weight using the string angle. Make sure the string angle is enough to position the table above the floor. Lift the table above your calculated height, add your necessary weight to the buckets then allow the table to lower and suspend at it’s equalized weight height.

By the way, a bosun's chair needs 2 men and a boy lifting, when anyone is sitting in it; you need to lift the weight of the chair as well as the person in it... Or! Normally you pull it up empty, tie it off then climb up and sit in it.

 

[TheVarsoTMLA]

If the angle between the rope and the table is theta when the buckets are in contact with the table then the weight of each bucket (m) must be at least equal to the weight of the table (M) divided by 4sin(theta).

m = M/[4sin(theta)]

See attached PDF.

 

[EricL]

This is simple. The weight of the table is equal to that of the buckets. A little push and you could make the buckets float 1 inch above the table. It would still be a static system and would not move.

Okay, even being a person with feeble math skills compared to anyone else here, I believe I see a problem with this statement, and I think I see this very thing being accounted for mathematically in some of the other replies (but I'd have to spend a day or two learning the math before I could be sure!). So, here's my take: I believe that each bucket must weigh more than 1/4 of the table's weight on account of the fact that the angle of the ropes relative to vertical is not the same on both sides of each pulley. If the rope on both sides of the pulley were vertical, your statement would be true (each bucket could weigh as little as 1/4 of the table's weight), but since the pulled-by-the-bucket leg of each rope is vertical and the table-lifting leg of each rope is angled away from vertical, it can't be true. Using my visual-only approach, it's easy to imagine increasing that angle away from vertical until the tension in the rope that's needed to produce the necessary upward lift becomes extreme, yet clearly the tension must be the same on each side of the pulley. Therefore, one needs to account for that decreased vertical component of the lifting force that's due to the table-lifting leg not being vertical, and that means increasing the load in each bucket by some amount. I'm sure some of the math-based replies provide a way of figuring exactly how much extra weight is needed, and the method I'd try first would be simple trigonometry. But don't forget that just to get the system to hold the position shown in the photo, "too much weight" in the buckets works just as well as "just enough."

Here's a related thought about having the system in perfect balance (defined as having "just enough" weight in each bucket). You say that "with a little push you could make the buckets float one inch above the table", but that's not true as I see it. In real life this could be done since the pulleys will provide friction, but assuming friction-less pulleys, as soon as you change the height of the table, you change the angle of the table-lifting leg of each rope, thereby changing the vertical component of the lifting force. In this case, if the system were perfectly balanced when the buckets were in contact with the table, moving the table to create a gap between the buckets and the table would reduce the angle away from vertical of the table-lifting leg of each rope, increasing the lifting force, thereby causing the table and buckets to come together once again.

Taking that one step further, if the system were perfectly balanced at a particular table height with the buckets not in contact with the table, if you manually displaced the table either upward or downward, it would drift back to its original position, since the lifting force provided by the ropes would be reduced when the table was raised, and increased when it was lowered. In actual fact, this principle surely aids in providing stability to the system (that is, the table is not prone to tilting).

If I'm missing something basic, shoot me down. Also, I'm sorry if this repeats anything that already was explained by someone using math.

 

[TheVarsoTMLA]

So, here's my take: I believe that each bucket must weigh more than 1/4 of the table's weight on account of the fact that the angle of the ropes relative to vertical is not the same on both sides of each pulley. If the rope on both sides of the pulley were vertical, your statement would be true (each bucket could weigh as little as 1/4 of the table's weight), but since the pulled-by-the-bucket leg of each rope is vertical and the table-lifting leg of each rope is angled away from vertical, it can't be true.

as soon as you change the height of the table, you change the angle of the table-lifting leg of each rope, thereby changing the vertical component of the lifting force. In this case, if the system were perfectly balanced when the buckets were in contact with the table, moving the table to create a gap between the buckets and the table would reduce the angle away from vertical of the table-lifting leg of each rope, increasing the lifting force, thereby causing the table and buckets to come together once again.

You're right! The buckets must be more than 1/4 the mass of the table. In this case they must be 1/4sin(angle between rope and table) the mass of the table. So if the angle formed when the buckets are in contact with the table was 60 degrees then the weight of the buckets would have to be about 1/3 the mass of the table. Take a look at the PDF attached for the math explanation.

 

[jaiswalshrey07]

Yes. See... the buckets are on the table. So the downward force exerted by each bucket is balanced by normal rxns. So the only force on the table now is tension. The total tension = total downward force (eqbm) and therefore, Tension = Tg+4Bg (where T and B represent Table's mass and a single bucket's mass).

 

[sophiecentaur]

You've been doing some digging!

So the only force on the table now is tension.

You can't get away without the weight force too.
Read through the whole thread and you'll find that pretty much all the relevant points have been dealt with. You'll also find quite a lot of confusion about operating a Bosun's Chair; I've used one several times so I know of which I speak. As a non-superman I needed assistance to actually raise myself.
Fact is that the buckets need only to weigh just more (total) than the table (plus other relevant gubbins) for the trick to work and for the buckets to stay in contact with the table. If the table is heavier then it will just fall down. Stability is a problem and three buckets would be better than four.

Carry on digging; there's some good stuff back there but a lot of it has been locked and needs reviving with new threads.

 

[Jeff Bigler]

I built one of these with one of my physics classes back in 2018. Here's a picture of it when I got it out this year. I put 2.5 L of water in each bucket, so each one weighed 25 N (probably plus an additional 1-2 N for the bucket and rope). After taking this picture, I put spring scales on each of the ropes that were attached to the table in the center, and each spring scale read 18 N. This means the normal force between the table and each bucket must have been 7 N, and the table must have weighed 54 N. After I poured the water out of two of the buckets, the table and the two remaining buckets were close to perfectly balanced, which further supports that conclusion.

 

[Hornbein]

I can't resist trying to come up with the simplest explanation.

Imagine that each weighted bucket were replaced with an eye bolt that the rope attaches to. It's pretty obvious the table won't go anywhere. The buckets are heavy enough to simulate eyebolts.

How heavy? The sum of the weight of the buckets must be greater than the weight of the table. Suppose you pile weights on the table. When the weight of the weights plus table is greater than the buckets' weight then the buckets will rise and the table fall. (Ignoring friction and assuming everything is perfectly balanced.)

 

[sophiecentaur]

I built one of these with one of my physics classes back in 2018.

I like it. Such good educational value. You can guarantee that pretty much EVERY student will be diverted and confused by that demo. And that's not something you could say about most of the things we show them!!

 

[renormalize]

Such good educational value. You can guarantee that pretty much EVERY student will be diverted and confused by that demo. And that's not something you could say about most of the things we show them!!

A tensegrity table would also impress students. (And it takes up less space!)