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Bettina
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If I take a bucket and begin filling it with tap water from a faucet, what would be the result if I kept moving the bucket up and down in the stream as it was filling verses keeping it stationary at the bottom of the stream. No water splashes out.

 

a) It would take less time to fill

b) It would take more time to fill.

c) It would take the same amount of time.

 

Bee

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If you're moving it up and down the same amount (that is, if the bucket isn't getting further and further away or closer and closer), then it would take the same amount of time. It must, as the same amount of water is coming out of the faucet per unit time, and all of it is going into the bucket. It will just fill slightly unevenly - faster when moving up, slower when moving down, but averaging exactly the same.

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The above is true if the bucket always starts at the lowest position. However, if you start the bucket very near the tap then it will fill up slightly quicker than if you start the bucket far away from the tap. Mostly, the extra time is accounted for by the duration it takes those first drops to reach the bucket. Close to faucet = short duration for first drops to hit. Far from faucet = longer duration for first drops to hit.

 

The movement of the bucket during the fill process has pretty much no effect.

 

However, the starting positions can, in fact, change the amount of time it takes to fill... Basically, because the water will take more time to go from faucet to bucket the farther away the bucket is.

 

You can eliminate that slight difference by having the water running and then putting it beneath the faucet (as opposed to placing the bucket underneath and then turning on the faucet as the next step).

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If there's no trick with the stream, I'm going to say that the bucket will fill faster if you hold it stationary, simply because you are creating air current by moving the bucket up and down, and that is going to cause a tiny extra amount of evaporation.

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The above is true if the bucket always starts at the lowest position. However, if you start the bucket very near the tap then it will fill up slightly quicker than if you start the bucket far away from the tap. Mostly, the extra time is accounted for by the duration it takes those first drops to reach the bucket. Close to faucet = short duration for first drops to hit. Far from faucet = longer duration for first drops to hit.

 

The starting positions wouldn't matter. It would be the ending positions that matter. The first drops of water are going to make it there long before its full no matter what.

 

This can all be ignored, however, if you just say the faucet will have to be running for the same amount of time no matter what.

 

If the bucket is close to the faucet, the last of the water will only have to fall a short distance after the faucet is turned off, making the bucket itself full very slightly sooner than if it is farther away - by the time it takes water (or anything) to fall that extra distance. Where it started or how it has moved in the intervening time don't matter, though.


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If there's no trick with the stream, I'm going to say that the bucket will fill faster if you hold it stationary, simply because you are creating air current by moving the bucket up and down, and that is going to cause a tiny extra amount of evaporation.

 

But could that evaporation be considered "splashing out" on a molecular level, and thus be discounted by the terms of the question?

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But could that evaporation be considered "splashing out" on a molecular level, and thus be discounted by the terms of the question?
"Splashing" from a faucet into a bucket of water implies water pushing water out of the bucket to fall to the ground. Evaporation is air vaporizing water out of the bucket, to travel generally upwards.

 

If a splash doesn't splash *on* something, can it still be called a splash? :confused:

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I took the no-splashing as just a rephrasing of the standard no-funny-business clause for logic puzzles, so that it'd cover evaporation.

 

Either way, I think it'll fill slightly faster. Since being kept stationary the distance from the tap will always be at the maximum ("bottom of the stream"), but being moved the average distance will be around the average of the minimum and maximum distance.

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"Splashing" from a faucet into a bucket of water implies water pushing water out of the bucket to fall to the ground. Evaporation is air vaporizing water out of the bucket, to travel generally upwards.

 

If a splash doesn't splash *on* something, can it still be called a splash? :confused:

 

The way I always understood evaporation was that the water molecules are jiggling around, and occasionally during this random motion one will break loose and mix with the air. It seems to me the equivalent on the macro scale would be choppy waves that occasionally splash upwards. So I maintain it's a splash. What it splashes on would, I guess, be whatever solid it eventually condenses on, after its journey being buffeted about by air molecules.


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Either way, I think it'll fill slightly faster. Since being kept stationary the distance from the tap will always be at the maximum ("bottom of the stream"), but being moved the average distance will be around the average of the minimum and maximum distance.

 

That would be true if each individual unit of water had to wait to leave the faucet for the preceeding one to reach its destination, but that isn't the case. It's a continuous stream. X units per second leave the faucet, so an average of X units per second must reach the bucket. The only wiggle room is the time after the faucet has been turned off, but before the last of it is done falling, i.e. the final position of the bucket. Average distance doesn't matter.

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The only wiggle room is the time after the faucet has been turned off, but before the last of it is done falling, i.e. the final position of the bucket.

I can't say that I agree with your point.

My main issue is that it seems to me that BOTH the starting AND ending position of the bucket are relevant.

 

If the bucket starts near the faucet AND ends near the faucet, the fill duration is minimized.

 

If the bucket starts away from the faucet AND ends away from the faucet, the fill duration is maximized.

 

If the bucket starts near the faucet then ends away from the faucet, it will be somewhere in the middle of the minimum and maximum fill duration (same if it starts away and ends near).

 

 

However, when I read your point, Sisyphus, you imply that starting position is irrelevant and end position is all that matters. Why do you propose this? I'm not seeing it (as described in my scenarios above). What could I be missing?

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Well ok. Let's say the faucet releases 100 units of water per minute, and the bucket has a capacity of 100 units. To fill the bucket, you need the faucet on for at least 1 minute. And to avoid spilling, you cannot have it on for more than 1 minute, as you will have released more water than the bucket can hold. So: no matter what, the faucet is running for exactly 1 minute.

 

Keeping that in mind:

 

First scenario: When you turn the faucet on, the bucket is 1 mile below the faucet. Some time in the next minute, you move it up to 1 foot below the faucet, taking whatever course you want (as long as its directly below the faucet, so you don't miss any). At the 1 minute mark, the faucet turns off, and you have gathered everything that came out of it, with the exception of that 1 foot of falling water. The total time is 1 minute + time for the last drop of water to fall 1 foot.

 

Second scenario: When you turn the faucet on, the bucket is 1 inch below the faucet. Over the course of the next minute, you move it down to 1 foot below the faucet, taking whatever course you want. At the one minute mark, you have gathered everything that came out of the faucet, with the exception of that last 1 foot of falling water. The total time is 1 minute + time for the last drop of water to fall 1 foot.

 

You see?

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Thanks for the interesting replies. I would have thought someone here would mention special relativity which is what my mind snapped to when I first heard this question. I thought of the bucket in motion vs the water in motion. Isn't that...though infinitely small... a factor too?

 

Bee

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Thanks for the interesting replies. I would have thought someone here would mention special relativity which is what my mind snapped to when I first heard this question. I thought of the bucket in motion vs the water in motion. Isn't that...though infinitely small... a factor too?

 

Bee

 

I guess it would depend on whether you were measuring in "Bee time" or "bucket time".

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Thanks for the interesting replies. I would have thought someone here would mention special relativity which is what my mind snapped to when I first heard this question. I thought of the bucket in motion vs the water in motion. Isn't that...though infinitely small... a factor too?

 

Bee

 

Catching water in a bucket moving at relativistic speeds would result in water vapor and a bucket with a hole in the bottom.

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Catching water in a bucket moving at relativistic speeds would result in water vapor and a bucket with a hole in the bottom.

 

At those speeds wont we overcome one of the forces in the standard model in regards to atoms and even possibly have a hydrogen bomb.

 

I really don't think the buckets movement would matter if the drip rate was constant and all the drips were going in the buckets volume.

 

Here at low position it takes 1.5 seconds for eighty drips to fill the bucket, and high it takes 0.5 seconds for the bucket to be filled, and at normal it takes 1.0 seconds for eighty drips to fill bucket.

 

At low its 1.5seconds x 80drips=full bucket=120 seconds

At high its 0.5seconds x 80drips=full bucket=40 seconds

At normal its 1.0seconds x 80drips=full bucket=80 seconds

 

So then it would be forty drips at high, plus forty drips at low=80 seconds. This is very rudimentary. You would have to know rate of travel, which that might increase in a giving distance, plus will all the drips be the exact equal mass, air pressure differences in the path of travel, would any rotation or minor shifts in the mass distribution in a drip cause any disturbance combined with hitting the atmosphere. I think the list can actually get very complicated rapidly, I think it would be fun to see a thread on this site that could actually factor everything out that would be in this question.

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Just a thought or two.

 

"Catching water in a bucket moving at relativistic speeds would result in water vapor and a bucket with a hole in the bottom."

All speeds are relativistic- some more so than others.

 

Imagine 2 taps and 2 buckets.

One bucket is just below the tap, the other is a zillion miles further down.

I turn on both taps and, in the time it takes to fill one of them, the water has yet to fall a zillion miles and reach the other.

The higher bucket fills first.

On average a bucket moving up and down is higher than one that's at the bottom of the stream. It should fill (marginally) faster.

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Just a thought or two.

 

"Catching water in a bucket moving at relativistic speeds would result in water vapor and a bucket with a hole in the bottom."

All speeds are relativistic- some more so than others.

 

Imagine 2 taps and 2 buckets.

One bucket is just below the tap, the other is a zillion miles further down.

I turn on both taps and, in the time it takes to fill one of them, the water has yet to fall a zillion miles and reach the other.

The higher bucket fills first.

On average a bucket moving up and down is higher than one that's at the bottom of the stream. It should fill (marginally) faster.

 

Where it is on average doesn't matter. One that starts right at the tap and then moves down to a zillion miles away will take exactly as fast to fill as one that stays a zillion miles away the whole time. One that starts a zillion miles away and moves to right under the tap won't take longer to fill than one that stays right under the tap the whole time.

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One that starts a zillion miles away and moves to right under the tap won't take longer to fill than one that stays right under the tap the whole time.

Yes, it would... At least if you start your timer from when the first unit of water leaves the tap as opposed to starting your timer when the first unit of water hits the bucket.

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Yes, it would... At least if you start your timer from when the first unit of water leaves the tap as opposed to starting your timer when the first unit of water hits the bucket.

 

If you start your timer when the first water leaves the tap, they will both take exactly the same time. If you start your time when the first water hits the bucket, the one that started a zillion miles away will fill faster, not slower.

 

Imagine one minute's worth of water is needed to fill the bucket. Imagine the bucket is a zillion miles away when the faucet turns on, and stays there for the next 59 seconds. Since water can't fall a zillion miles in 59 seconds, no water has reached the bucket yet. In the next second, it flys at a zillion miles per second and moves right up against the tap, thereby gathering all the water in midair as it moves.

 

As measured from first-water-in-bucket to full, the zillion miles away bucket fills in one second. As measured from tap on to full, it fills in one minute, just like the bucket that was against the tap the whole time.

 

Of course, if the bucket stays a zillion miles away, then it will take exactly one minute from first water in bucket to full. As measured from tap on to full, it will take 1 minute + however long it takes water to fall a zillion miles.

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Of course, if the bucket stays a zillion miles away, then it will take exactly one minute from first water in bucket to full. As measured from tap on to full, it will take 1 minute + however long it takes water to fall a zillion miles.

 

Precisely. :)

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Isn't the question "how long does it take to fill the bucket"? Not how long does the faucet run. The bucket doesn't start filling until the first water enters it. Its true that the if the bucket is far below the faucet when the faucet is turned on, there is a time lag before it starts filling. Same for when you turn the faucet off, i.e. there is a time lag between turning the faucet off and the bucket being filled. If the bucket is close to the faucet, that water goes in with almost no delay. So there is a time difference in water entering the bucket. The shortest time to fill the bucket would be starting with the bucket low down, and finishing high up, and vice versa.

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