That’s a wonderfully-constructed classic that I can still remember hearing for the first time as a child.
And it pretty much explains the physics of what we’re talking about.
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… but what if i fill my buckets with lead, gold or uranium. It should be possible to set it up so that if i step on the table that the combined table and me weight is still less than that of the buckets. and it will not go move. (unless it rips the bolts out of the ceiling and comes crashing down)
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Or the buckets get so heavy that they break the table. Most kitchen table tops are not meant to hold up buckets of uranium, I don’t think.
Quick, someone who knows something, what breaks first?
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I’d lay money on the bucket handles being first to fail, not break
I’d say it depends on if the table is solid wood or Ikea. 
Most people’s understanding of gravity is limited to “gravity pulls things down.” And most people don’t really get, intuitively, how pulleys work. And your list is missing a few points that are very obvious to you and me, but weren’t stated explicitly by anyone for the first few thousands of years of people using ropes and weights.Just because people know the words and have seen the effects doesn’t imply deep enough understanding to interpret a new, unusual case.
- Tension - Ropes work by transmitting force from one end to the other.
- Reaction force - the buckets push down on the table, and the table pushes up on the buckets. Lots of people know the words “equal and opposite reaction” who have never seen F=ma, J=pv,a free body diagram, or even an algebraic equation.
- Vectors. The idea that forces have associated directions, or that you can separate out the horizontal and vertical components of the force when analyzing a system, or how adding forces pulling in different directions together will play out, is not obvious.
- Pulley systems.Yes, there is a reason why first semester college physics students have problems sets evaluating what happens to the masses attached to various kinds of Atwood’s machines - and typically getting them wrong at first even though they have received explicit instruction in all the rules the system obeys.
- Force as an abstract concept. Most people think “solids hold things up because stuff can’t pass through them” or something like that. They don’t think of the table pushing on whatever it is holding, to balance the force of gravity trying to pull those things down.
I guess I’m coming at this from a different angle. A professor I briefly worked with as an undergrad spent a substantial amount of his time researching physics education, measuring just how confused physics students (at Harvard, primarily) were about basic concepts like inertia - like showing them pictures of someone walking at constant speed and dropping a ball from their waist, and asking if it will hit the ground next to, in front of, or behind them.
And really, if you think this is all so obvious any first grader with a pulley can work it out, ask Aristotle how an arrow flying through the air works. I hear he was a pretty bright guy.
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“…If the left side of Cliff Clavin’s brain is on a train heading East at 50 mph…”
I am not a physicist, but I find that an intuitive explanation of normal force. And why, if you increase the difference between the weight of the buckets and the weight of the tables, you increase the force that they exert on each other instead of passing through each other.
Nope – you could have completely frictionless pulleys at the top and it would still work.
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I’m another one who is mildly surprised that this takes so much analysis. I never had a Physics class, nor could I put the proper name to most of the forces at work, but having actually used pulleys before, the whole setup seems utterly simple to me. At first glance, I knew that (unless things weren’t as they seemed, as in buckets-fastened-to-tabletop, or ropes-made-of-stiff-cable, or similar foolishness) I could walk up to the table, press down upon the center of it, and the buckets would probably all rise evenly, unless combined they were substantially heavier than the table in which case I’d have to press harder. If I press down on one side of the table, the two buckets on that side would rise, the table would tilt, and there’d be a decent chance the other two buckets would begin to slide toward my side of the table, which would also encourage the table itself to slide out from under them in the opposite direction. Lengthening or shortening all four ropes equally won’t make much of a difference. Lengthening <4 ropes so as to make the table tilt will make it easier for the setup to lose equilibrium and the buckets to slide off, not just because a bucket of water is more likely to slide off a tilted shelf, but also because the downward force of the buckets against a slanted surface will push that slanted surface sideways, encouraging the table to slide out from under the buckets.
It’s a funny test of mindsets. Maybe I have an unusually good sense of spatial relationships and forces, maybe I’ve hung too many weird Halloween props from ropes and pulleys, but my intuition screams that this is not a counterintuitive setup at all.
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Sorcery, obviously. Now if it had only dispensed with magical pulleys and incorporated the true physics of a buttered cat …
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My cat just flops on his side and refuses to do anything.
I’m kind of surprised that nobody pointed out that the tension in each of the ropes is one-eighth of the combined weight of the buckets and table.
…well, to correct myself- a little more than an eighth since the ropes are not plumb.
I’d say all those terms you use are not helpful - actually they probably only confuse most people. The physics are understood intuitively with a problem like this, and I’d wager it could be explained to a first grader. As @Donald_Petersen points out, if you think about how the table got to this position, or what would happen if yo push down on the table, it’s pretty clear what’s happening. The analysis of forces and vectors is only really useful for using this as a way of explaining more complex problems.
I get what you’re saying though - I remember spending an hour in a junior level college physics class trying to convince another student that a bomb dropped from a plane would continue traveling forward (like your dropped-ball explained). It’s astonishing how little some people know, but it’s more of a result of just not thinking about things much, I reckon.
What a great short - did not end the way I thought it would at all.
And many people are missing the point (shown clearly in moooooo’s analysis) that the angles of the ropes through the pulleys are important. As a result of this, making the ropes shorter can make the table fall even when everything else is equal to a stable situation.
And the action of changing the lengths of the ropes was part of the problem specification. No one who relied strictly on intuition was therefore able to answer the question completely.
It doesn’t seem like anyone using pure intuition has yet taken into account the angles between the ropes and the tables. Since the buckets can only transfer their weight times the sine of this angle to the vertical force on the table, shortening the ropes can make the situation unstable because it decreases this angle. Some aspects of trigonometry may be explainable to certain first graders, but probably not very many.
There’s 4 possibilities:
- The table is stable as is.
- The table falls enough so that the buckets hit the ceiling.
- The table falls a little bit but becomes balanced with the buckets as the angle between the ropes & the table changes.
- The table hits the floor.
There’s 3 major parameters:
X. The initial angle between the ropes and the table
Y. The weight of the buckets compared to the weight of the table
Z. Some ratio between the height of the ceiling and the length of the rope.
Since I only want to plot in 2D, I’ll leave out the case where the table hits the floor & thus ignore parameter Z. Then I think this is the solution:
Just keep in mind the table may hit the floor for the “unstable” cases depending on how far away the floor is.
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I am almost certain the person who created this piece at no point calculated the sine, or used any equation remotely like yours. Your mathematical explanation is entirely correct, I just don’t think its necessary to explain this work.
