The "Bowling Ball in a Boat" Paradox
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- čas přidán 11. 05. 2024
- If you're in a boat and you drop a heavy ball into the water; will the water level go up, go down, or stay the same. Solving this requires Archimedes Principle, Newton's Laws, and some logic.
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TIME CODES
00:00 Cold Open
00:27 Common Answer
00:56 Some Bowling Balls Float
01:22 Experiment 1 (Floating Ball)
02:00 Mechanical Equilibrium
02:23 Archimedes Principle
03:19 Experiment 2 (Sinking Ball)
04:13 Explanation 2 (Sinking Ball)
04:41 Extreme Solutions
05:46 Rigorous Solution
06:27 Free Body Diagram of Ball
07:06 Summary
07:43 Featured Comment
In b4 people wrongly claim that it's not a paradox without actually knowing what a paradox is.
Oh and in case anyone doubts this, here's a definition from Merriam Webster: "a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true"
That would suggest that for many, the word paradox is in fact a paradox!
@@unvergebeneid "opposed to common sense" Except it is common sense. And by that definition anything can be a paradox to anyone given the right knowledge and beliefs.
People claiming it's not a paradox are operating under the definition of a logical paradox. You citing MW just makes you seem condescending. Do you really not know what a logical paradox is or are you just being disingenuous?
@@captianmorgan7627Look, your problem isn't with me, it's with the English language. I can't help you there.
Lesson learned: Make sure not to inadvertently create neutronium, since that can ruin your experiment.
And your day :P
It's a good thing I watched this video first, as I was just about to try that!
I learned this lesson the hard way, I made some neutronium and now my house is in a billion pieces.
ikr. That experiment escalated quickly.
@@davidspencer2729 And your next upwards of 80 years.
The key to figuring this out is understanding not only that floating objects will displace their own mass of water, but also realizing that objects which SINK cannot displace a volume of water greater than that object's own volume. So basically, once an object is dense enough to sink, it doesn't matter if it's a bowling ball, or solid tungsten, it will only displace its VOLUME of water, not its mass.
That said, with a boat to support it, it IS floating, not sinking. Therefore with the ball in the boat, the boat+ball system is displacing its total mass of water, but once the ball is thrown overboard, the ball can no longer displace its mass, only its volume. Because a unit volume of "ball" weighs more than a unit volume of water, less total water is displaced afterwards, resulting in a lower water line.
Very nice explanation
yup, density and volume. The weight only matters when it is on the boat
I think the _key_ is the math Nick showed us, but yeah, as a layperson, I just remember that floating things displace their mass and sinking things displace their volume. I'm not 100% sure about things that float after submerging entirely, like a boiled egg in saltwater, though. Intuitively they should displace water by volume, but given the math and the fact that its upward vector is all the buoyant force of the water underneath it rather than the buoyant force plus the normal force, I'm thinking it might displace by mass?
It does not matter... Unless it's neutronium!
But an 8-pound ball and 16-pound ball have the same volume. So these balls individually displace *same* volume. For the 16-pound, that displaced water isn't enough to balance its weight, and it sinks.
So even though the latter sinks and former floats, their same volume would displace the same level of water individually.
That's the thought I am getting. Like could you tell what am I not taking in mind ?
Instead of compressing the bowling ball, it might be easier to compare a 16 pound ball and a same-sized 100 pound ball. Both displace the same amount of water when in the lake. But when they are in the boat, the 100 pound ball would push the boat deeper into the water, displacing more water and raising the lake's level.
yeah, that 100 pounds gets "diluted" onto the boat's volume, causing an "equal" amount (in volume, and therefore mass) of water to get displaced in order to counterbalance the "new" weight
Ok it makes sense now. Thanks for the clarification. The video wasn’t as clear.
Of course, if the ball is heavy enough, it will submerge the boat, causing it to displace much less water. Also the ball would be submerged anyway in that scenario.
the water level of the lake will not be effected by the bowling ball
Superb explanation! I remember my undergrad physics prof explaining something similar using equations only, and I didn't get it. Your home-made props made it look so simple. Nice job Nick.
Thanks Arvin!
Two great science educators on one comment. Awesome!
Another easy way to explain is that when it's in the boat, it's displacing as much volume of water as the ball weighs. Out of the boat, it's displacing its own volume of water. Since it sinks, the amount of water that weighs the same as the ball must have a greater volume.
right at the poin, ruining all the fun
Tbh I was still grinding my gears trying to understand why less water would be displaced when the ball sinks.
I think I was imagining two balls with a set volume, but different weights. The one that is floating, well only half of it is in the water so the water should be displaced less. But I was thinking about it wrong. The point is that compared to when it was on the boat, if it sinks there's less displacement.
Not that there's less displacement when an object of equal volume sinks because it's heavier.
Wow! Thank you!
Yeah. I think Nick makes it a bit too complicated. Anyone who knows how things float would figure it out easily.
@@Secret_Moon You might be surprised. I used to scuba and asked every dive master I went with this question, and the few who got it right couldn't explain why. :-) It's not as intuitive as it seems after you already know the answer.
1:13 Today I learned that Nick Lucid really does have actual clones, it's not just camera trickery.
The real question is, why do smaller bowling balls float? Are they made of less dense material? I assumed it was the same material, just less of it.
The materials are all _similar,_ but mixed in different proportions.
Less of the same material in the same space means it's less densely packed.
Bowling balls are standard size, but made of multiple layers. The weight of a ball is set by the ratio of outer shell with a less dense inner core.
I was going to ask "but what if the boat also sinks", but I'm glad to see you experimentally verified that!
Ah I see you are a true mathematician, looking for a general solution rather than just an answer to the question.
My best bet is.. same as bowling ball. If the boat has component that is heavier than water, then it displaces less water, water level will be lower.
The key to this problem is to know that floating objects displace their WEIGHT in water irrespective of their volume, while sinking objects displace their VOLUME of water irrespective of their weight.
Yeah this is not a paradox at all...
Nobody has ever explained buoyancy so perfectly, I’ve never really truly understood it til now
Glad I could help 🤓
Can we just appreciate the editing at 1:20? That one had me rolling.
Let’s take a look at the floaters first.
They are brown, all have sunk and are ready to convert into flowers somewhere in the sewer.
I think originally it was a cannon ball, but since the pirates today are not interested in paradoxes, or something, it switched to bowling ball.
Also, it's not true that you cannot rise water level without adding something to the system. Just pick up the ball from the floor of the lake. Unless you consider it outside of the system, but then you also remove the ball from the system when it sinks to the bottom.
@@ItsActuallyTJ_ Then dropping the ball is removing the energy. Picking it up is reverse of dropping it, so one cannot work and other don't, in this regard.
The water does rise though when the ball floats. A little bit but it does. The volume of water displaced remains the same but the part of the bowling ball that sticks out of the water is now space unavailable to be filled with water and therefore the water level has to rise a little bit. It's the same amount of water but in a slightly different shape which brings the water level a bit higher.
I miss these types of videos, it reminds me of the good old days when you did the bucket of water and merry go round experiments
I miss those days too. I'm making an effort to get some of that fun back. Lost it somewhere along the way.
I actually went to the opposite extreme to prove the same thing: pretend the vessal has no weight, and just barely floats with the ball inside it. When you take the ball out of the boat and put it in the water, the boat no longer displaces any water, so it goes from the entire volume of the boat being displaced to just the volume of the ball, which always has to be smaller.
Oh! This is a _great_ way to handle it! 🤓 🤘
Most shocking part for me was realizing some bowling balls float. Sure, it makes sense now that I think about it. But still surprised me.
a solid anvil will float in mercury
@@brownie3454But if you smith a bowling ball on it and roll a strike, will the mercury level go up, or down?
@@quokka_11 there would be spare mercury for sure
@@brownie3454I'm not so sure. I guess we're split on that.
@@quokka_11 Time to strike out the puns, guys.
So Nick has a real cloning machine after all, everything is making sense XD
I love this example very much. A friend of mine brought it to me once. And she summarized it as: "When floating, the ball displaces its mass, when sinking, it displaces its volume." I find this the sharpes summary of the effect that I have heard so far.
Thanks for the video, gonna share it with mentioned friend :-). Hope you are fine!!
I saw this one in a different video a few years ago :P while it's in the boat, a dense object displaces it's weight in water, but when you drop it off the boat, it only displaces its volume. So dropping any object denser than water off the boat will cause the water level to fall.
If you go to take a bath or go to a boat you always need: a lantern, a rubber ducky, an umbrella and a bowling ball. Everybody knows that. have you ever watched Ernie and Bert?
But no towel. That's for space travel.
I always watch Bert and Ernie bathe. Always..... where’s my lotion?
Rubber duckie, you're the one! (And about to put the hammer down.)
You and your clone both reacting to the poop joke was genius, and the absurd neutronium edge case was incredibly relevant!
My first thought is that it depends on the density of the ball. The ball is assumed denser than water. In the boat only the ball's weight matters, so it will displace a greater volume of water than its own. But when it is in the water, it can only displace a volume of water equal to its own. Therefore the level will go down.
Post Edit. Doh! Being a totally non-sporting person, I had no idea that there could be a bowling ball less dense than water.
Honestly, I'd never heard this one before. It's easier to understand than the one I remember from high school: the weight of a jar with a fly sealed inside.
This is similar to the "birds in a truck" thought experiment, that Mythbusters turned into a real experiment. Since the birds push air downward to stay aloft, that downward air pushes on the floor of the truck. At equilibrium, the downwash from the birds flying will be equal the normal force from the birds standing on the floor with their feet, and the truck would weigh the same even with the birds flying.
This makes so much sense why things feel lighter under water untill you take it out
WATER: "If you push me, I'm going to push you back!"
I absolutely loved this! I thought I knew the answer until you said it depends on if the bowling ball floats or sinks... Then I realized I knew the answer but not for the right ball and had to flip my way of thinking about displacement/buoyancy (and bowling balls). That's the paradox! Pretty sneaky.
I'm glad you found it stimulating 🤓. It's one of my favorite questions for students.
I am studying chemistry and that was a question i got in my physics 1 and 2 test. It was a really short one with a low amount of points but still funny to see it here after 3 weeks
It was one of my favorite questions to give to classroom, though I usually gave it as a group problem because I got the best results when students were allowed to discuss with each other.
I appreciate "the lake demands sacrifice". I don't know if you intended it this way, but it reminds me of the relationship of volume under the water and weight of water displaced. Sinking objects seem to cheat, they don't offer enough submerged volume to displace equivalent weight. Meanwhile the boat pays its fair share of surface area for its weight. Maybe it's like poker and "all in" can be enough when the amount itself isn't.
All the math means nothing to me but with the visuals and explaining I can understand how it all works, thankyou. Super interesting.
Thanks! I tried to cover the topic every way I could in this video.
I thought at first that the water line meant the water line on the boat, where it would obviously go down any time you got rid of a bowling ball
Same. I feel like this should be an important distinction.
I like that the clone laughed as well.
The rules are simple:
When an object floats, it displaces an equal WEIGHT of water
When an object sinks, it displaces an equal VOLUME of water.
Since 1 kilogram of water = 1 liter of water, I will use those units.
Take a bowling ball with a volume of 0.5 liters, but a weight of 1 kg (making it twice as dense as water)
When floating in the boat, it displaces an amount of water equal to its weight (1kg of weight which equates to 1 liter of water by volume).
Because it sinks when taken out of the boat, it displaces an amount of water equal to its volume (0.5 liters).
So it displaces 1 liter in the boat, but only 0.5 liters in the water, meaning it takes up 0.5 liters LESS volume, ergo the water level goes down.
Doesn't it depend on how many Nick clones are sacrificed to the Lady of the Lake?
This was a question on the pre-enrolment placement test to determine what physics class you should enter, at Caltech in 1986. (I got it.)
When trying to lead people to the answer, I suggest starting with two nested Solo cups (representing the lake and the boat) and a heavy coin in the inner cup (the bowling ball). Fill the minuscule volume between the two cups with water, and the inner cup barely rises. Move the coin to the outer cup, and all the water falls down, buoying up the inner cup.
initial guess before watching, is that it would depend on the density of the bowling ball
to float a boat is to displace water equal to the weight of the object being floated (bit more complex but thats the simple explanation)
so if you have a 15lb bowling ball on the boat, 15lbs of water is displaced and the water level rises the weight of the rest of the boat+cargo and 15lbs. when throwing it off, the boat displaces 15lbs less of water than it did before, but the bowling ball in the water is now displacing a bowling balls volume worth of water, which should be less than the 15lbs of water
(avg bowling ball is ~1.45 gallons, ~5450 CC, so the water displaced would be 1.45 gallons, or around 13 lbs worth of water. so the water level would be slightly lower
however, if the bowling ball was floating, the water level would stay the same, as it would have the same effect in or out of the boat, floatin is floatin is floatin
These are the best kinds of brainteaser questions. Where there's a naive answer (water goes up), a smart answer (water stays the same), and a correct answer (water might go down), which are all different.
Two others like this are "will a plane on a converyor belt take off" and "if a coin lands heads 20 times in a row, what are the odds it will land heads again?"
I was sceptical, but your illustration with changing the volume of the ball quickly helped me understand: the floating ball or any ball in the boat is fully accounting for the displacement of bowling ball's mass. But if the bowling ball sinks, it can't displace as much water as its mass is capable of. Thanks Nick!
This water displacement experiment must have taken place at Lake Brunswick.
Here's an interesting thought. You can measure volume with scales. If you suspend an object in a container of water, the weight of the container will go up by the buoyant force the object experiences. Since the buoyant force is determined by the density of the water and the volume of the object, the density of the object won't matter. If the weight goes up by ten grams in water at 1g/cc, the volume was ten cc's.
Note that it doesn't matter if you suspend an object that will sink from above, say with a bit of fishing line, or if you suspend it from below, anchored to the bottom. Pretty cool, eh?
The easy part is the claim that if you toss the ball into the air and it lands in the water. The water level will go down then back up as the ball leaves the boat and goes into the water (wether it floats or sinks)
It's interesting to learn that if it sinks it drops the water level but not if it floats (stays the same)
My guess is that the density of the bowling ball is higher then the combined boat-ball. So it lowers.
Edit: Ok, I didn't think any bowling ball would float.
Surprise! 🤓
@@ScienceAsylumIndeed
This is something new, Glad to be early too.
I'm tired of being stuck in a creative box 👍. Thought I'd step out of it for a bit.
Great explanation, Nick. Density relative to water helped me also.
That is exactly what baffled me when I was a kid with Archimedes' principle. I was only focusing on the concept of volume; logically a crown of brass or a crown of gold would displace the same amount of water if the two are equally submerged in water. It was unclear for me how he could effectively make the difference.
I didn't thought about mass, like if you compare both crowns in say your "boat" and register separately the water level.
Great video, well explained.
I assume you're referring to the of verifying if a crown is made of solid gold or not? In that case the volume measurement is combined with a weight measurement to get the density of the crown's material, and that is how you can check if it's gold or not.
Yeah, yeah, the physics and math is cool and all. But all I'm taking away is that bowling balls float.
High-five for the neutronium digression. 100% worth it. You could have used that footage from the 1947 dump of 20,000 lbs sodium into Lake Washington as the clip.
Oh, that would be have been good! Oh well.
"We're gonna need a bigger boat " - that just got me.
Love to see new videos Nick. Thank you!
I'm relieved that soon after getting an engineering degree, my intuition for this question was right. I'd probably have to throw out my $100,000 piece of paper if I was wrong.
My Physics teacher told me, if you don't know answer to a fluid mechanics problem, mark the opposite of what you think will happen, it will most probably be correct.😂😂😂😂
😂😂 Good advice! If you can't get the physics, you can at least predict how your teacher would set up the question.
This is a great version of this question. If I remember correctly, Veritasium’s version involved a Diamond trapped inside an ice cube.
"Who doesn't have a bowling ball in their boat." - Damn straight.
The sinking ball displacing less water when it sinks than in the boat works also the opposite way. The boat can displace less than the ball that floats on its own if its surface tension is spread out more. It's like using more pillars to support a roof. It might still float in the water, but it displaces more volume because it's not designed to float it's only lighter that the mass of the water for its volume.
Not sure what you are saying but it doesn't sound correct. The surface area of the boat doesn't matter. A floating 100kg boat displaces 100kg of water whether it's small or large in area. That's kind of the point of the video. Floating objects displace their entire mass, but sinking objects only displace their volume, irrelevant of mass.
@@GigsVT It's misunderstanding surface tension properties to think that a floating object displace their entire mass. Some of it is negated by the density of the water particles. It's not gravity that rules the sinking or floating, it's surface tension. It would work the same without gravity albeit not pulled towards one direction. If the boat float it's precisely because it doesn't transfer all its mass into the water, and its volume allows surface tension to take effect. That's why surface tension in a boat with a large hull overall displaces the water less than the sum of its objects floating on their own. The mass only matters if their is actual sinking, otherwise it's the floating volume present below the surface of the water that matters for the level of water and that is the amount of displacement introduced in the water. Technically if you have a bunch of polystyrene on a boat then the water would rise when you put the polystyrene inside of the water, because suddenly it would float better than it does in the boat, where the mass matters more than the volume. It truly depends on the objects floating properties and volume to mass ratio. It's not mass vs volume, it's an equilibrium of them all.
@@metasamsara Where have you heard this? Surface tension only needs to be accounted for when considering very low masses relative to the area of the water's surface they are spread over.
What If Mars and Venus were replaced by identical clones of Earth similar to our planet
Noice
What if Mars and Venue were replaced by identical clones that were not similar to our planet? Now that's an interesting question.
what if we terraform Venus and make Mars a Disney Theme Park ?
It would be _possible_ for each to sustain life, but that life would be different since it would have to adapt to the temperature differences.
@@charlievaneit better be a roller coaster ride to get to Disney land Mars
You're living my dream. You are an inspiration! Thank you for making awesome entertaining videos!
Another similar and fun puzzle: if you're standing on a highly accurate scale and you place your finger into a cup of water placed on a nearby surface (not on the scale) what happens to your measured weight? And if the cup is also on another accurate scale, what would happen to its measured weight?
Well????.....Tell us the answer.
@@kw8757 can't figure it out? : )
😇😇 that's something new .
true
😇😇😇
I'm tired of being stuck in a creative box 👍
@@ScienceAsylum😊😊
Mr Lucid, thank you for all your videos. I have watched all of them numerous times. I really wish you would have, like, 3 million subs. Please keep up the excellent quality work ❤❤❤🎉
We called it the "brick in a boat" problem, but essentially used this same question while interviewing mechanical engineers.
That certainly removes some ambiguity.
Poop jokes
I donʼt think you need the full Archimedes Principle or Newtonʼs Laws for this. Just the simple fact that a floating object will displace a volume of water with the equivalent weight is enough to solve it. You can derive that from the Archemedes Principle and Newtonʼs Laws, but itʼs often taught and understood by itself. With that, you can see the amount of water displaced by a heavy bowling ball in a boat would have the mass of that ball, but the amount displaced by the ball at the bottom of the lake would have to only have the volume of the ball.
Amazing approach to this riddle. I'm not quite sure if I already understood fully, but it's cool.will rewatch the video in parts 😎🫶🇩🇪
I like to think in extremes. If the bowling ball weighed 1million pounds, it woukd displace one million pounds of water, far less than the volume of the bowling ball. So the water level woukd go down when the ball is taken from the boat and dropped in the water.
Thinking extremes makes it so much easier to visualize
I could have used this video 15 years ago. A coworker asked me this question using a brick instead of a bowling ball. He insisted the water level would stay the same. I recognized that the brick's mass is what pushed the boat down, but the brick's volume was what would displace water when outside the boat, so I said it would go down. The argument lasted for days until I gave up after realizing I was never going to convince him mass and volume were not the same thing.
_A lot_ of people think of mass and volume as the same thing. It's a very prevalent misconception.
The quote from the soundtrack of "Soul Reaver" was the cherry on the cake!
Rawrsome! one of the best EP...love phyics here!
The water level would go down, very slightly. Floating above water in a vessel, the ball displaces a volume of water equal to its weight. IN the water, the ball displaces only its volume. Since the ball weighs more than an equal volume of water, The volume of water displaced would be less when it is in the water than when floating above it.
3:34 "We're gonna need a bigger boat" That was the most perfect possible response!
😂 We were having a good time.
Incredible video. Much appreciated.
depends on the density of the ball, and a few other esoteric state of the two main version of the situation:
in the boat, as long as the boat is a boat and floats, the ball exerts its full weight down the boat, and displace the same weight of water. if the boat turn into a submarine, we have a different version, lets ignore that.
in the water, the ball displace its volume. so if the density is one g/cm3, this will be the same volume of water, so the level will not change. if the density is higher, than the volume of the ball is smaller than the volume of the same weight water, and the level will sink (well, in theory, practical change is negligible), if the balls density is lower than water, than its volume is higher than the same weight of water, but it will also float on water. so in this case we have to separate if we force the ball into the water or not. if not, than only the enough water will be displaced to tits weight, so the level stays the same. if we force the ball into the water, than obviously more water will be displaced, rising the level.
About the accretion disk question at the end, recall that the image we receive of the visible disk is warped by the black hole's gravity. The bright spots, at least to some degree, may be influenced by this warping.
just started the video, and im saying the water will stay the same. my hypothesis is that the boat is displacing some water, and when the bowling ball is dropped, the boat will be displacing less water, but the bowling ball itself is still displacing that water. cant wait to see if im right.
Edit: turns out i was right, but only for balls that float. i didnt expect the water level to go down if the ball sinks, but the "dust particle sized bowling ball" example helped me understand what was happening.
I remember an old variant that was a real 'mind-bender'. Instead of a lake, suppose your boat is in a small canal lock. For simplicity, assume your boat is 10x20 rectangle, and the lock that it's in is 12x24. Now, you dump something 'heavy' over the side of your boat. Something like rocks that is much denser than water and sinks (assume a specific gravity of 2.0). Initially, the deck of your barge/ boat is even with the top of the canal wall. How much rock (by weight) do you have to dump over the side to raise the deck to be 6 inches above the canal wall?
Like shown in this video, dumping the weight from the boat to the bottom of the lock will lower the water level. But taking weight off the boat/ barge will raise the deck level. So....
P.S. Assume the boat/ barge sides are vertical and several feet high such that the displacement area doesn't change with draft.
I am an early sub. This channel grown so much and it really inspires me as a small content creator. Keep the Asylum Running!!!!
Thanks for sticking around!
I wouldn't've considered the force perspective of displaced water volumes, which makes this a novel approach for me.
Personally I would've considered it like this: when the mass is in the boat, the volume of water displaced by the boat increases by the amount of water required to offset the new mass and the same holds true for all positively buoyant objects; however, the sinking object does not have sufficient volume to displace water equal to its own mass so the water level would change as the displacement of water decreases.
Same ideas, just looking solely from the perspective of displacement.
@ 4:54 Yessss. Take it to extremes. Classic strategy, and exactly how I solved it. @5:20… make sure to take BOTH extremes. Pretty unusual for a solution to work in the extremes but not between. Happens sometimes.
Considering that this is the first problem ever presented to me by Physics girl this hit home in a different way.
If the column of water is deep enough, the 16 pound ball will find equilibrium just by displacing water. The water it displaces will be compressed from above and weigh the same as the ball. In this scenario the water level will remain the same.
Great video. Makes me motivated to post my video on a Vos Savant puzzle of how you can float a giant ship with a gallon of water, showing you don't have to literally displace as much water as the mass of the ship if you use a dry dock almost exactly the shape of the ship.
A floating object displaces its weight in water, a submerged object displaces its volume. If the ball is denser than water, then the former displacement is greater than the latter
So so interesting! Love classical physics! Well done
Very well explained. Kudos to you! I'm probably not the first one to comment this, you could have added the notion, that once the ball is heavier than what the system of the water can support for it to float, the ball becomes part of the system of the container that holds the water.
Interesting, my "extreme version" is to manipulate the mass of the object instead of the volume, and that makes it more obvious to me. A ball more dense than water in water doesn't matter if the ball's mass is 1kg or a 1000kg mass ball, the volume of water displaced is exactly that of volume of the ball, and the weight is obviously lower since water is less dense. When the ball was on the boat, its the entire system's mass is displacing an equal amount of water, which has to be a higher volume since because you need more volume of the less dense water to match the ball's mass. So this configuration has to be higher.
So, it only _seems_ like a paradox until you understand the mechanics of it. I had a very solid lightbulb, "Aha!" moment here; thanks for that!
The lake demands a sacrifice, because the lake gods want to go bowling.
Thanks for the informative material, it's always a good feeling to understand our world and it's workings just a little bit better.
I had a question like this on a physics final in college, but it was with a flat piece of plate steel in a boat (so there was no question of its buoyancy outside the boat).
A similar example like this is a block of floating ice. If there is just ice, the level of water after it melts and before is the same. But say there is a stone frozen in the ice, or kept above it, then after the ice melts, the level of water comes down.
This example was given by our professor (along with the one in the video)
Doing the math is always the most correct and rigorous way, but there are other ways to look at this that actually make the problem fairly intuitive, if not just plain obvious. Basically all you need to know is:
1. Any (unsupported) object in water will displace _up to_ the amount of water needed to match its weight (if it can).
2. If it can displace the same amount of water as the object weighs, then the object will float (with the extra volume the object has beyond the displaced water volume sticking up above the water)
3. If it cannot displace enough water to equal its weight (because the object does not have that much volume), then the object will sink.
Therefore, _if the object is floating_ then by definition it is displacing exactly the amount of water that equals all of the weight of the object. It doesn't matter how it is floating (whether it's in a boat or not), this will always be true. _If the object sinks_ then it is because it was displacing _less water_ than was needed to match its weight. As long as the weight is the same as before, if it was floating and is now sinking, it must be displacing less water than before.
By extension, if the total weight of everything involved has not changed (still 1 boat + 1 bowling ball), but before all of it was floating and now only some of the weight is floating (and some has sunk), then everything taken together must be displacing less water in total than it was before.
There is an abundance of science based educational and info-tainment based youtube videos. What advice would you give about discerning which ones provide accurate information from which to learn from. Love what you do, thank you!
That's a tough question. If it were easy to discern who was reliable, I think we'd have a lot fewer misinformed people. Here are some of my thoughts on it:
*Green Flags*
1. They have relevant college degrees or they've cited experts.
2. They include reputable sources in the video description (or on screen).
3. They self-correct when their errors are exposed.
*Red Flags*
1. They define themselves in opposition to others. (Their brand is "debunking" other scicommers, They "know better" than the scientific consensus on a subject, etc.)
2. They promote obvious hoaxes like perpetual motion machines or something.
3. Their videos lack any nuance at all. (Lacking _some_ nuance is fine. See below.)
You should also be aware of the educational level a scicommer is targeting and decide if you're in that target audience. This can vary depending on the topic. But, if you're looking for a deep explanation, an over-simplified but _confident_ general audience video can easily mislead you. That doesn't necessarily mean the "general audience" scicommer did anything wrong. It just means the video wasn't _for you._ There are a lot of highly-skilled viewers that treat this as a red flag and give scicommers hate they don't deserve.
Another factor to consider is how new they are to scicomm. My early work often didn't have reputable sources included and lacked all nuance. These were lessons I learned over the years. So, if a mistake isn't too egregious, it might be fair to cut the newbie some slack.
(my answer pre-watching) Assuming the bowling ball is denser than water(sinks), the water level will go down. (*if the ball is less-dense than water, it will stay the same. because all floating objects displace only their weight in water. until you get so light, that surface affects take over)
---(if it sinks)Floating objects (boat and ball in boat) displace their weight of water. sinking objects displace their volume of water. (denser/sinking objects weigh more than their volume of water)
-So, the ball when in a boat is displacing its weight in water. (lets say the ball is 5kg, so 5kg of water). Now, when the ball is in the water(sinking objects), it displaces its Volume of water, not its weight in water. We assumed earlier the ball is denser than water, so its volume must be less than the (weight of its) volume of water. Lets say the volume of the ball is 500cm3. 500cm3 of water is 4kg, 500cm3 of ball is 5kg. the volume of water displaced by 5kg (when ball is in boat) is 625cm3. the volume of water displaced by the ball (when under water) is 500cm3. Volume of ball(500cm3), vs volume of water of weight of ball (625cm3). the ball was displacing 625cm3 when in the boat(higher water level), and only 500cm3 in water(lower water level). So the water went down by 125cm3 when the ball was sunk into the water.
---(if it floats) floating objects always displace their weight of water. floating in the boat it would displace 500cm3 of water, and floating it would displace 500cm3 of water. water level stays the same.
Well done! 👍
First thoughts: The boat has to displace water to float. A heavy weight would push down more on the boat, displacing more water. If instead, it is dropped off the side of the boat into water, it would only displace the volume of the bowling ball. Inside boat, weight, outside boat, volume. I'm guessing if something weighs more per volume than water, the least displacement would be in the water. Assuming the bowling ball is denser than the water, it would displace less while in the water.
Addition after watching the video: So basically right. Yes, a floating ball only displaces the amount of the ball below the water line. My answer also assumes, as demonstrated in the video, that the boat can still float while supporting the ball.
Sometimes your intuition informs your math, and other times your math informs your intuition.
hearing "Hey Crazies!" in a new video just makes my day
Trying to come up with an answer before watching the video:
Boats float and bowling balls sink.
Floating things displace their mass in water, sunken things displace their volume in water. Taking the bowling ball out of the boat will lowee the water level by the amount of water that has the mass of a bowling ball. But dropping the ball in will raise the level by its volume in water. Since bowling balls are denser than water (I would assume so, anyway) then the amount raised will be less than the amount lowered, therefore the water level will lower.
When I imagined this, I took density to the extreme by imagining the bowling ball had a ridiculously large mass. I like your approach better because it doesn't risk sinking the ship.
This is a good exercise in that it forces people to be cognizant of the system itself and how that can influence phenomena. It’s very easy to assume a person would be outside it.
Exactly!
Inside the boat the ball is displacing the volume of water that is the save weight as the ball.
Once you drop it out of the boat it is only displacing the volume of the ball itself and that must be less or the ball would float.
Therefore the water level goes down.
I'm convinced that Science Asylum are identical twins and not CZcams editing.
when placed in the boat, the weight of the ball is added to the amount of water displaced ( boat will sit lower in the water, thus "raising" the water )
when dropped over the edge, the mass will be removed from the boat, which will lower the amount of water displaced ( boat will float higher up on the surface, thus "lowering" the water )
so the water would go down from the boats perspective
edit: assumed it was about the waterlevel from the boats perspective, as a boat is seldom located inside a container ( yes, technically it kinda is, but the surface is usually big enough that the displacement from a single small boat couldnt be practically measured)
the observation still holds up, just that the water level goes up even more, by the height of a shape shaped like the surface of the water with a hole cut out for the boat, with the bowling balls volume