Ahh, explained in terms even I can understand. Two questions remain: one, how irresponsible is it to let two girls inhale Sulfer Hexafluoride? Two, in the Japanese clip, why did the balloon sink? I'm assuming it has something to do with boyancy.
Rather than answer your question, I will ask another more interesting question that Steve was asked in a job interview at Apple. (I hope I remember this correctly).
You are in a boat floating in a pool. There is also a heavy rock in the boat which you pick up, drop into the pool, and watch sink to the bottom. Does the level of the water in the pool go up, go down, or stay the same?
I thought about this again and it occurs to me that this was too trivial for an Apple interview. (Although I must say that I looked up the question on the web after I posted it, and almost everyone gets it wrong! Apparently they forget that the boat with the rock is already displacing pool water. All they see is a rock thrown into a pool, so the water must go up by the volume of the rock. This saddens me in that 1) we haven't improved our knowledge of buoyancy/displacement since Archimedes' time and 2) our own self deception is so great that we're willing to display it on the web.)
Anyway, I'm beginning to think the real question may have been: Compared to the edge of the pool (i.e. the ground), does the boat rise or fall or stay the same?
I may be incorrect but your question lacks the needed information. Since the height of the water and buoyancy force are not directly related.
Also don't get too sad,
1) Our (humanity) knowledge of buoyancy has greatly increased- Archimedes principle is only applicable to static liquid forces (can't be applied to items sinking or floating to the top) and also Archimedes never took into account surface tension, application to gases etc. As for individual knowledge, when is the Archimedes principle needed? The knowledge to me is about as relevant as the latest Eminem Album (meaning since our brain are not endless, individuals will pick and choose knowledge they retain). 2) Humans make mistakes and misunderstand things and thats okay. Especially on the internet because others will correct you and you may learn something you never had really cared about.
Even if they were surfing the web while the teacher was talking Archimedes, a little imaginative thinking on their part would help—probably what the interviewer was after.
They could think of the rock as shaped like a heavy keel and attached to the bottom of the boat. Dropping the rock/keel doesn't raise the water level at all since it was already submerged, but the boat is lighter so it displaces less pool water. Water goes down, boat goes up.
Another way to think of it, often a useful technique, is to consider the extreme situation. Consider the case where the rock is so dense that, although it submerges the boat to its gunwales and pushes the displaced water up to the edge of the pool, it is microscopic in size. Now its easy to visualize that throwing the rock out of the boat will have a negligible effect in raising the water level by displacement (it's microscopic), but a huge effect dropping the water level since the boat is now hugely lighter and floats higher displacing much less water.
And I'm going with Pete in thinking that those hundreds of people, who lemmings-like wrote "up" in answer to the water question, have all returned to the site, seen their mistake, been intrigued by the mysteries of life and science, and now have all become engineers or research scientists.
For clarification, I know the answer to the first question, I was referring to your second question, "Compared to the edge of the pool (i.e. the ground), does the boat rise or fall or stay the same"? The height of the boat relative to the ground is dependent on two things. First, the height of the water displacement which in turn is dependent of the length and width of the pool. Second, the buoyancy force which is not dependent on the pool size instead on the average density of the water and of the boat. Therefore, I think you have to give one variable to get an answer to your second question.
Yeah, I'm not sure about the second question myself.
And, you're right that the size of the pool determines how high the water lowers or rises. But, it seems to me that (perhaps) in all cases the boat would rise more than the pool water would go down. Here I think knowledge of Archimedes is useful. Since the boat is floating it is always displacing a volume of water equal to its mass. If water is thrown out of the boat, then nothing would change—the water would 'rise/fall' the same amount the boat would 'rise/fall'. But if the object is denser than water is thrown out the volume of water displaced is less than the rise of the boat.
Obviously in an ocean this is trivial, the boat rises more than the ocean level will fall, but in the extreme case where the boat practically fills the pool, I think this also would be true. Actually I was so unconvinced that I tested it with a cup in a bowl of water. I still will not say I have scientific certainty, but I believe the boat will always rise more than the pool will fall.
gahhhh...I couldn't figure it out mathematically. All I needed was an instance where the boat stayed the same relative to the ground thus giving two answers (rises, stays the same). It appeared with Archimedes math that the boat would rise more than the decrease in water level, however I thought to myself what is the temperature of the rock versus the water, at what temperature would the water need to increase decreasing the density of the water thereby negating the rise of the boat resulting from decreased density. Also, does the rock have water soluble compounds in it which would increase the density of the water and therefore cause the boat to rise maybe offsetting the increase in water temperature....brain just exploded.
Ha ha. Now that is classic. I see a whole new realm of puzzles. He takes the rock from the ship and throws it into the water and the boat sinks to the bottom of the pool. How does that happen? As you have hinted, the rock is so hot it vaporizes all the water in the pool!
I'll let someone else come up with one where the rock turns the pool to a thick mud or oobleck-like substance.
16 comments:
Mind = Blown
Here is the more understandable children's version.
Ahh, explained in terms even I can understand. Two questions remain: one, how irresponsible is it to let two girls inhale Sulfer Hexafluoride? Two, in the Japanese clip, why did the balloon sink? I'm assuming it has something to do with boyancy.
Rather than answer your question, I will ask another more interesting question that Steve was asked in a job interview at Apple. (I hope I remember this correctly).
You are in a boat floating in a pool. There is also a heavy rock in the boat which you pick up, drop into the pool, and watch sink to the bottom. Does the level of the water in the pool go up, go down, or stay the same?
I should add, Steve answered correctly, of course!
Stays the same. No. Goes d-- Auuuuuuuugh!
Don't fret Myk, Oppenheimer and Gamow answered incorrectly though I am about 99% sure science hadn't invented water at that time.
If Steve got it right, does that mean that he's smarter than both George Gamow and Robert Oppenheimer?
I thought about this again and it occurs to me that this was too trivial for an Apple interview. (Although I must say that I looked up the question on the web after I posted it, and almost everyone gets it wrong! Apparently they forget that the boat with the rock is already displacing pool water. All they see is a rock thrown into a pool, so the water must go up by the volume of the rock. This saddens me in that 1) we haven't improved our knowledge of buoyancy/displacement since Archimedes' time and 2) our own self deception is so great that we're willing to display it on the web.)
Anyway, I'm beginning to think the real question may have been:
Compared to the edge of the pool (i.e. the ground), does the boat rise or fall or stay the same?
I may be incorrect but your question lacks the needed information. Since the height of the water and buoyancy force are not directly related.
Also don't get too sad,
1) Our (humanity) knowledge of buoyancy has greatly increased- Archimedes principle is only applicable to static liquid forces (can't be applied to items sinking or floating to the top) and also Archimedes never took into account surface tension, application to gases etc. As for individual knowledge, when is the Archimedes principle needed? The knowledge to me is about as relevant as the latest Eminem Album (meaning since our brain are not endless, individuals will pick and choose knowledge they retain).
2) Humans make mistakes and misunderstand things and thats okay. Especially on the internet because others will correct you and you may learn something you never had really cared about.
Even if they were surfing the web while the teacher was talking Archimedes, a little imaginative thinking on their part would help—probably what the interviewer was after.
They could think of the rock as shaped like a heavy keel and attached to the bottom of the boat. Dropping the rock/keel doesn't raise the water level at all since it was already submerged, but the boat is lighter so it displaces less pool water. Water goes down, boat goes up.
Another way to think of it, often a useful technique, is to consider the extreme situation. Consider the case where the rock is so dense that, although it submerges the boat to its gunwales and pushes the displaced water up to the edge of the pool, it is microscopic in size. Now its easy to visualize that throwing the rock out of the boat will have a negligible effect in raising the water level by displacement (it's microscopic), but a huge effect dropping the water level since the boat is now hugely lighter and floats higher displacing much less water.
And I'm going with Pete in thinking that those hundreds of people, who lemmings-like wrote "up" in answer to the water question, have all returned to the site, seen their mistake, been intrigued by the mysteries of life and science, and now have all become engineers or research scientists.
For clarification, I know the answer to the first question, I was referring to your second question, "Compared to the edge of the pool (i.e. the ground), does the boat rise or fall or stay the same"? The height of the boat relative to the ground is dependent on two things. First, the height of the water displacement which in turn is dependent of the length and width of the pool. Second, the buoyancy force which is not dependent on the pool size instead on the average density of the water and of the boat. Therefore, I think you have to give one variable to get an answer to your second question.
Yeah, I'm not sure about the second question myself.
And, you're right that the size of the pool determines how high the water lowers or rises. But, it seems to me that (perhaps) in all cases the boat would rise more than the pool water would go down. Here I think knowledge of Archimedes is useful. Since the boat is floating it is always displacing a volume of water equal to its mass. If water is thrown out of the boat, then nothing would change—the water would 'rise/fall' the same amount the boat would 'rise/fall'. But if the object is denser than water is thrown out the volume of water displaced is less than the rise of the boat.
Obviously in an ocean this is trivial, the boat rises more than the ocean level will fall, but in the extreme case where the boat practically fills the pool, I think this also would be true. Actually I was so unconvinced that I tested it with a cup in a bowl of water. I still will not say I have scientific certainty, but I believe the boat will always rise more than the pool will fall.
gahhhh...I couldn't figure it out mathematically. All I needed was an instance where the boat stayed the same relative to the ground thus giving two answers (rises, stays the same). It appeared with Archimedes math that the boat would rise more than the decrease in water level, however I thought to myself what is the temperature of the rock versus the water, at what temperature would the water need to increase decreasing the density of the water thereby negating the rise of the boat resulting from decreased density. Also, does the rock have water soluble compounds in it which would increase the density of the water and therefore cause the boat to rise maybe offsetting the increase in water temperature....brain just exploded.
Ha ha. Now that is classic. I see a whole new realm of puzzles. He takes the rock from the ship and throws it into the water and the boat sinks to the bottom of the pool. How does that happen? As you have hinted, the rock is so hot it vaporizes all the water in the pool!
I'll let someone else come up with one where the rock turns the pool to a thick mud or oobleck-like substance.
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