# Really 'interesting' puzzle • Page 2

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• Destria 16 Oct 2013 10:45:44 2,861 posts
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 It does make the steel ball appear to be lighter though, so *something* must be supporting it. That's the water. The water isn't heavier, but the bathtub is now supporting the combined weight of the water, and some of the weight of the steel ball. I think, anyway. I'm going to try my scales experiment and see what happens.
• Destria 16 Oct 2013 11:10:03 2,861 posts
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 Well, air is compressible for one, so they're not exactly comparable. It's also not in a confined area. Air is also a lot less dense anyway. I'm not sure mind, so I'm going to try this out at home. See what happens with some scales. But Googling to find the answer to this just found a Reddit full of people disagreeing with each other.
• Deleted user 16 October 2013 13:45:08
 LeoliansBro wrote: Buoyancy is a complete red herring. No it isn't. If I dangle a steel ball in my bathtub full of water it doesn't make the bathtub full of water heavier. Yes it does. Again, this is literally something you can test yourself using scales and a container filled with water. Dip your hand in. Does the reading on the scale increase? (hint - yes it does) Or, to put it another way, is the tension on the string less if the ball is submerged? (hint - yes it is). If so, where does that tensile force go? (hint - conservation of force)
• Destria 16 Oct 2013 15:56:46 2,861 posts
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 meme wrote: Again, this is literally something you can test yourself using scales and a container filled with water. Dip your hand in. Does the reading on the scale increase? (hint - yes it does) Well that's my evening's entertainment spoiled . (I'll still do it, just to confirm my own sanity).
• Deleted user 16 October 2013 16:30:55
 There's an equal amount of water being displaced, but the steel ball is not at the point of flotation like the ping pong ball is (IE, it's denser than the water that surrounds it), so it pushes downwards with a greater force than the ping pong ball. Seriously, now. Do the scale thing. Put in a heavy object. Then put in a light object.
• Mr_Sleep 16 Oct 2013 16:37:09 21,530 posts
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 Am I being thick in suggesting that the ping pong ball is full of air and so it wouldn't be possible to submerge it from above without applying the necessary force which would then tip the scale that way? Or is it being submerged in some other method?
• Deleted user 16 October 2013 16:40:01
 The string doesn't counter the entire downward pressure of the steel ball (see previous remarks about tension a few posts up). The ping pong ball doesn't have this advantage, as it's not actually putting a downward pressure on the water due to it being less dense and wanting to rise, rather than sink. It's all about the balance of forces based on mixture of systems (the beakers, the scales, the crane holding the steel ball). Once again, this is literally something you can actually demonstrate with very basic household equipment. Don't make me record a video.
• Fatiguez 16 Oct 2013 16:43:32 8,882 posts
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• Deleted user 16 October 2013 17:04:37
 We don't have to disagree. (EDIT - I had something here about buoyancy but I think it just confuses the issue more. It's more about unequal systems than buoyant forces themselves). PHYSICS. The problem you're hung up on is the mistake I made with my first explanation - the ping pong ball beaker is an enclosed system, whereas the steel ball beaker is a system with an external system overlapping it. Forces have to balance out (third law), but the systems themselves are not equal. One last attempt: The crane suspending the steel ball feels a force. That force is the downward pull of the steel ball (ie its weight). The steel ball is submerged in water. The crane feels less of a force. By Newton's Laws that force has to have gone somewhere (after all, the mass of the ball hasn't changed, the gravity of the earth hasn't changed, so its actual weight (w=mg, or the downward force in Newtons) is the same), and that somewhere is into the water itself. Third Law = every action has an opposite and equal reaction, so as the water supports the steel ball (IE, it pushes up on the steel ball), the ball itself pushes down on the water. The upward force applied by the water goes into the crane. The downward force applied by the ball goes into the scale. Any additional forces the pingpong ball applies beyond weight are negated by it being an enclosed system (if it pulls up on itself, it also pushes down on itself, etc etc). Edited by meme at 17:19:21 16-10-2013
• Destria 16 Oct 2013 17:47:19 2,861 posts
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 Yes. System on the left clearly weights the same regardless of the presence of the ping-pong ball or not (assuming zero weight ping-pong ball and string). Otherwise you could produce an amazing mug with a ping-pong ball in it attached via string that made a litre of water magically weigh less. The ping-pong ball on the left is effectively doing what you'd be doing if you grabbed your ankles and tried to make yourself lighter by tugging. Edited by Destria at 17:48:55 16-10-2013
• Deleted user 16 October 2013 18:13:11
 Just because I'm that bored, I worked out some of the physics. The equation, effectively, is "does the change in tension of the string supporting the steel ball when immersed in water exceed the weight of the ping pong ball?" A ping pong ball weighing 2.7g will, in weight, add a force of 0.025 newtons downward. For argument's sake we'll say the volume is 8000mm cubed. Remember that buoyancy doesn't apply to the pingpong ball container, as it's an enclosed system balanced out by Newton's Third Law. An 8000mm cubed sphere of steel weighs about 63 grams, and applies about 0.6 newtons downward. So if there's more than a 5% reduction in tension on the string (or if the buoyancy forces exceed 5%), the right side will drop as it will exceed the force the pingpong ball's weight is applying to the lefthand side of the scale. For an 8000mm cubed sphere, and a water density of 1,000kg/m3, the buoyancy force is 0.08 newtons. Which is little over 10% of the weight of the steel ball. Which is greater than 5%, which means the right side will drop. QED motherfuckers. Edited by meme at 18:15:19 16-10-2013
• Fake_Blood 16 Oct 2013 18:21:26 8,182 posts
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 The steel ball doesn't influence the system besides displacing just as much water as the ping pong ball, all forces cancel out, the system is in balance.
• grey_matters 16 Oct 2013 18:28:14 4,341 posts
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 meme wrote: Just because I'm that bored, I worked out some of the physics. The equation, effectively, is "does the change in tension of the string supporting the steel ball when immersed in water exceed the weight of the ping pong ball?" A ping pong ball weighing 2.7g will, in weight, add a force of 0.025 newtons downward. For argument's sake we'll say the volume is 8000mm cubed. Remember that buoyancy doesn't apply to the pingpong ball container, as it's an enclosed system balanced out by Newton's Third Law. An 8000mm cubed sphere of steel weighs about 63 grams, and applies about 0.6 newtons downward. So if there's more than a 5% reduction in tension on the string (or if the buoyancy forces exceed 5%), the right side will drop as it will exceed the force the pingpong ball's weight is applying to the lefthand side of the scale. For an 8000mm cubed sphere, and a water density of 1,000kg/m3, the buoyancy force is 0.08 newtons. Which is little over 10% of the weight of the steel ball. Which is greater than 5%, which means the right side will drop. QED motherfuckers. Nice. How long is a piece of string? And more importantly how heavy? Edited by grey_matters at 18:28:41 16-10-2013
• Deleted user 16 October 2013 18:28:33
 The system is in balance...but the system is "beaker plus crane" on the right hand side and just "beaker" on the left. The scales, however, only feel the forces acting on the beakers, not the forces acting on the crane. Seriously, I'm right here. I've literally just proven it with maths. There's 0.08 newtons of buoyancy force that's applied to the steel ball (and thus the crane), which according to 3rd Law means there's 0.08 newtons applied to the beaker (and thus the scale) in return.
• masc.box 16 Oct 2013 18:32:33 127 posts
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 meme wrote: Just because I'm that bored, I worked out some of the physics. The equation, effectively, is "does the change in tension of the string supporting the steel ball when immersed in water exceed the weight of the ping pong ball?" A ping pong ball weighing 2.7g will, in weight, add a force of 0.025 newtons downward. For argument's sake we'll say the volume is 8000mm cubed. Remember that buoyancy doesn't apply to the pingpong ball container, as it's an enclosed system balanced out by Newton's Third Law. An 8000mm cubed sphere of steel weighs about 63 grams, and applies about 0.6 newtons downward. So if there's more than a 5% reduction in tension on the string (or if the buoyancy forces exceed 5%), the right side will drop as it will exceed the force the pingpong ball's weight is applying to the lefthand side of the scale. For an 8000mm cubed sphere, and a water density of 1,000kg/m3, the buoyancy force is 0.08 newtons. Which is little over 10% of the weight of the steel ball. Which is greater than 5%, which means the right side will drop. QED motherfuckers. I think I love you.
• X201 16 Oct 2013 18:40:07 18,335 posts
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 meme wrote: Just because I'm that bored, I worked out some of the physics. The equation, effectively, is "does the change in tension of the string supporting the steel ball when immersed in water exceed the weight of the ping pong ball?" A ping pong ball weighing 2.7g will, in weight, add a force of 0.025 newtons downward. For argument's sake we'll say the volume is 8000mm cubed. Remember that buoyancy doesn't apply to the pingpong ball container, as it's an enclosed system balanced out by Newton's Third Law. An 8000mm cubed sphere of steel weighs about 63 grams, and applies about 0.6 newtons downward. So if there's more than a 5% reduction in tension on the string (or if the buoyancy forces exceed 5%), the right side will drop as it will exceed the force the pingpong ball's weight is applying to the lefthand side of the scale. For an 8000mm cubed sphere, and a water density of 1,000kg/m3, the buoyancy force is 0.08 newtons. Which is little over 10% of the weight of the steel ball. Which is greater than 5%, which means the right side will drop. QED motherfuckers. /paging Spindizzy Peer review required. Spindizzy found the Higgs Boson*, so his word on the matter is final. * some other people helped a little as well.
• grey_matters 16 Oct 2013 18:44:19 4,341 posts
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 Hmmm, a Ping Pong ball has a radius of 20mm. Volume is about 33000mm^3. Edited by grey_matters at 18:51:56 16-10-2013
• Destria 16 Oct 2013 18:47:37 2,861 posts
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 masc.box wrote: meme wrote: ### an amazing explanation ### I think I love you. I saw him first! The reduction in the tension of the string will basically be equivalent to the tension required to support the water displaced, as that's the buoyancy force applied to the ball.
• Deleted user 16 October 2013 18:48:03
 If the volume of a ping pong ball is 33000, the volume of the steel ball also increases (becoming around 260 grams), so the maths still works out. Edited by meme at 18:49:42 16-10-2013
• grey_matters 16 Oct 2013 18:51:10 4,341 posts
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 meme wrote: If the volume of a ping pong ball is 33000, the volume of the steel ball also increases, so the maths still works out. I think it makes you even more right. The bouyancy (of steel ball) should also increase. You'd need a pretty heavy string to balance it out. Edited by grey_matters at 18:55:27 16-10-2013
• Rusty_M 16 Oct 2013 18:55:06 6,779 posts
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 meme wrote: Just because I'm that bored, I worked out some of the physics. The equation, effectively, is "does the change in tension of the string supporting the steel ball when immersed in water exceed the weight of the ping pong ball?" A ping pong ball weighing 2.7g will, in weight, add a force of 0.025 newtons downward. For argument's sake we'll say the volume is 8000mm cubed. Remember that buoyancy doesn't apply to the pingpong ball container, as it's an enclosed system balanced out by Newton's Third Law. An 8000mm cubed sphere of steel weighs about 63 grams, and applies about 0.6 newtons downward. So if there's more than a 5% reduction in tension on the string (or if the buoyancy forces exceed 5%), the right side will drop as it will exceed the force the pingpong ball's weight is applying to the lefthand side of the scale. For an 8000mm cubed sphere, and a water density of 1,000kg/m3, the buoyancy force is 0.08 newtons. Which is little over 10% of the weight of the steel ball. Which is greater than 5%, which means the right side will drop. QED motherfuckers. Most intelligent POTD ever.
• mal 16 Oct 2013 19:05:05 29,077 posts
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 The way I see it is that on the left hand of the scale you have a beaker, a ping pong ball and a bit of string connecting the two, and an amount of water. On the right you have, resting on the scale, a beaker and the same amount of water. Cross out the beaker and the water from both sides, and you end up with the string and ping pong ball extra on the left. That said I've not yet tested Gremmi's fist in a bucket test result. But it quacks like a lot of the mumbo jumbo presented in this thread so I'll be surprised if it, er, holds any water. Edit: But while I'm away testing, I'll leave this for Meme to think through: what has the tension of the steel ball string have to do with anything? The steel ball is not moving - it's in equilibrium. So, Newton's third law applies. The ball is exerting a mass downwards which is resisted by an equal and opposite pull from the string. To offset this pull in the string, the support pulls it up by the same amount and so on. It doesn't matter how big this force is - there's always an equal and opposite force resisting it (until your string breaks or the support stand falls over). Edited by mal at 19:13:33 16-10-2013
• Deleted user 16 October 2013 19:18:10
 mal wrote: what has the tension of the steel ball string have to do with anything? It's supporting the weight (IE the force) of the steel ball. If the tension of the string decreases, it's no longer supporting the entirety of the force. That force doesn't just disappear, it goes somewhere. Where does it go? Into the water. Look, I'll repeat myself: The crane suspending the steel ball feels a force. That force is the downward pull of the steel ball (ie its weight). The steel ball is submerged in water. The crane feels less of a force. By Newton's Laws that force has to have gone somewhere (after all, the mass of the ball hasn't changed, the gravity of the earth hasn't changed, so its actual weight (w=mg, or the downward force in Newtons) is the same), and that somewhere is into the water itself. Third Law = every action has an opposite and equal reaction, so as the water supports the steel ball (IE, it pushes up on the steel ball), the ball itself pushes down on the water. The upward force applied by the water goes into the crane. The downward force applied by the ball goes into the scale. Any additional forces the pingpong ball applies beyond weight are negated by it being an enclosed system (if it pulls up on itself, it also pushes down on itself, etc etc). Edited by meme at 19:20:27 16-10-2013
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