What will happen to the water level of the swimming pool?

[Ravi Singh choudhary]

if the person sitting in the boat throws a pebble to the swimming pool. Pebble was initially contained inside the boat and of course it has higher density than water.

 

[CWatters]

What do you think will happen and why?

 

[Ravi Singh choudhary]

The density of boat will become low after throwing the pebble. Therefore boat will rise decreasing the level of the water in the swimming pool but at the same time stone is inside swimming pool again displacing some volume that means water level will be the same.

 

[rcgldr]

The boat displaces water based on the boats total weight and density of water. The pebble is denser than water.

 

[Ravi Singh choudhary]

The boat displaces water based on the boats total weight and density of water. The pebble is denser than water.

So what's the conclusion

 

[rcgldr]

Lost an edit to my last post. Posting here. Think of this as another clue.

When the pebble is in the boat, all of it's weight is supported by the buoyant force of displaced water. When the pebble is resting on the bottom of the pool, some of it's weight is supported directly by the bottom of the pool.

 

[billy_joule]

Cosider the extreme case and the problem is much easier to understand;
The boat is weightless and the pebble has close to infinite density.

 

[Ravi Singh choudhary]

Cosider the extreme case and the problem is much easier to understand;
The boat is weightless and the pebble has close to infinite density.

That means initially boat and pebble was drowned, displaced volume is (volume of boat + volume of pebble). When pebble is thrown, boat will rise to the top and boat's bottom surface will just kiss the water surface and pebble is drowned only; so this time only displaced volume is volume of the pebble. Am I correct in the interpretation of weightless boat and pebble of infinite density?

 

[billy_joule]

A boat can support near infinite weight without sinking, it just has to be very large.
The boat will only sink if we constrain its size in some way, if we let the boat sink the question is very different, and IMO losses the interesting aspect.

The weightless boat and very dense pebble has the same result as the question in your OP, it's just that the extreme case makes the outcome much more dramatic/easier to understand.

 

[CWatters]

Perhaps focus on the very dense pebble part.

 

[rcgldr]

displaced volume is (volume of boat + volume of pebble). When pebble is thrown ... only displaced volume is volume of the pebble. Am I correct in the interpretation of weightless boat and pebble of infinite density?

The second part is correct. For the first part (pebble in boat), the displaced volume is the volume of water equal to the weight of the boat and the pebble.

 

[A.T.]

...time stone is inside swimming pool again displacing some volume that means water level will be the same.

How did you get from "some" to "same"?

 

[hsdrop]

It seems to me that the boat is what confusing. All the boat does in this case is add bounce to the rock. Allowing it to float which means that some of the total surface of the rock is out of the water at this point setting the level of the water. Then you take away the boat or at least take away the bounce of the rock. The rock sinking to the bottom getting completely covered in water making the level of the water go up. You can also look at the question like this. Say you have a ball that you can add and subtract sand from. when the ball is empty the ball floats taking up less space in the water. When you fill the ball makes it sink. The ball takes up more space in the water making the water level go up. From my point of view the question is one of volume and all the rest of info is just there for continuity of speech. Real life or word problems always have extra info. You just have to figure out what the base math is in the problem and everything else is useless info

 

[A.T.]

All the boat does in this case is add bounce to the rock. Allowing it to float which means that some of the total surface of the rock is out of the water

When in the boat, the entire rock surface is dry, but the rock can still be completely below the water level.

 

[hsdrop]

When in the boat, the entire rock surface is dry, but the rock can still be completely below the water level.

you know i could wipe the rock in cellophane. keeping the rock dry at the bottom of the water Then call the cellophane the boat the question does not ask if the rock gets wet or not it asks what the level of the water when the rock is at the bottom of the water compared to floating on top

 

[A.T.]

i could wipe the rock in cellophane. keeping the rock dry at the bottom of the water Then call the cellophane the boat

That would be a submarine though.

 

[hsdrop]

lol very true
by definition: to float on or in water the sum of the parts have to be less dense than the water. Everything that floats has some part is out of the water and that would lead you to think that when pushed down (either by a finger or grative) the water would have to rise ? you did say the boat is wireless which means that the boat does not displace any water on its own. rock bears the total load of the boat and rock when in the water so you take away the waterless boat (the upward force on the rock making it float) and the rock sinks I'm just looking at the boat as a way to lesson the density of the rock

 

[Stephanus]

That means initially boat and pebble was drowned, displaced volume is (volume of boat + volume of pebble). When pebble is thrown, boat will rise to the top and boat's bottom surface will just kiss the water surface and pebble is drowned only; so this time only displaced volume is volume of the pebble. Am I correct in the interpretation of weightless boat and pebble of infinite density?

A boat can support near infinite weight without sinking, it just has to be very large.
The boat will only sink if we constrain its size in some way, if we let the boat sink the question is very different, and IMO losses the interesting aspect.

The weightless boat and very dense pebble has the same result as the question in your OP, it's just that the extreme case makes the outcome much more dramatic/easier to understand.

It doesn't have to be. The volume of the pebble has to be very, very small to sustain the wieght of a "normal" pebble.
As long as it's not below $2GM/c^2$ or it will evaporate all the water in the swimming pool, and hopefully not the entire city.

 

[A.T.]

the water would have to rise ?

If that's your conclusion, then something is wrong with your reasoning.

 

[olivermsun]

lol very true
by definition: to float on or in water the sum of the parts have to be less dense than the water.

To float on or in the water the parts must have density less than or equal to the water.

Equal (neutral buoyancy) is just the limiting case where the object must displace all the water it can possibly displace to achieve a balance between gravity and buoyancy.

 

[olivermsun]

i could wipe the rock in cellophane. keeping the rock dry at the bottom of the water Then call the cellophane the boat

That would be a submarine though.

Sinking to the bottom is not usually the desirable mode of operation for a submarine!

 

[hsdrop]

If that's your conclusion, then something is wrong with your reasoning.

did you read my reasoning?? Please do not just point at something and say it wrong. It would be much more helpful to everyone that are trying to learn if you explained why it was wrong

 

[A.T.]

It would be much more helpful to everyone that are trying to learn if you explained why it was wrong

Try applying some actual physics:
https://en.wikipedia.org/wiki/Archimedes'_principle

 

[hsdrop]

Try applying some actual physics:
https://en.wikipedia.org/wiki/Archimedes'_principle

that still lives it up to the reader to try to figure out what was wrong with my thinking

It would be much more helpful to everyone that are trying to learn if you explained why it was wrong

 

[A.T.]

that still lives it up to the reader to try to figure out what was wrong with my thinking

It doesn't use physics, just vague associations.

 

[hsdrop]

ok I have tried being polite with this in asking how and why my logic was wrong. please keep in mind that I'm not at all trying to argue that I was right or not. I have how ever been asking for a specific reason why I'm wrong so I can learn and others reading this can learn from my misthinking as well. but if all you're going to do is answer with "vague associations" to my thinking it will not help me or anyone else at all. it one thing to point out that someone is wrong. but if me or anyone else is going to learn from this it would be much more effective if you gave a specific reason (with the example given) why it is wrong

 

[A.T.]

but if me or anyone else is going to learn from this it would be much more effective if you gave a specific reason (with the example given) why it is wrong

Apply Archimedes' principle to the scenario. Then you can revisit your previous arguments yourself to see where they went wrong.

 

[hsdrop]

i did try to do that that's why i keep asking where i went wrong to my understanding the question is a question of valium and not one of bouncey because it asks if the water level goes up or not

 

[A.T.]

i did try to do that

So what did you get for:
- Water displaced by boat with stone
- Water displaced by boat without stone
- Water displaced by sunken stone

I don't see where you derive those quantities.

 

[hsdrop]

The weightless boat and very dense pebble has the same result as the question in your OP, it's just that the extreme case makes the outcome much more dramatic/easier to understand.

a weightless boat would not displace any water till something is put on it
the mass placed on the boat would just displace the water for the mass
but you're saying that if the mass was submerged the water level would stay the same no matter what the volume of the mass is(provided it would sink and not float on it own)??

 

[rcgldr]

Try some example numbers, like the mass weighs 1,000 kg, and has a volume of .05 m^3 (1/20th cubic meter). When the mass is in the boat, how much water is displaced? When the mass is resting at the bottom of the pool, how much water is displaced?

 

[CWatters]

...but you're saying that if the mass was submerged the water level would stay the same no matter what the volume of the mass is(provided it would sink and not float on it own)??

Check again. Did he really say that?

 

[hsdrop]

ok now I'm starting to see what the water level would do. it just the way the question was given had me a little mixed up
also i am a veary slow at read (i have a savear reading disablety with decoding) and i just now got to the boddom of the https://en.wikipedia.org/wiki/Archimedes'_principle page that gives a detaled explanchen on how and why the principle works witch help emancely

 

[hsdrop]

Check again. Did he really say that?

and you're right i looked and no he did not say that

thank you everyone for being so patient with me

 

[Charles Link]

Interesting problem. I don't know if the OP's question ever got answered, but when the rock is in the boat it will cause an extra displacement of water equal to its weight. If the density of the rock is greater than the density of water, the amount of water displaced by the rock when it is in the boat will be greater than the volume of the rock. When the rock is thrown in the water, it sinks to the bottom and the rock only displaces its volume. Thereby the water level of the pool holding the boat drops a small amount. Alternatively, if the rock is less dense than water, it will float (it won't be entirely submerged) when tossed out of the boat and the amount of water displaced by the rock will be the same whether it was in the boat or out of the boat.

 

[Ravi Singh choudhary]

Now what I understood reading the complete thread. Boat is assumed weightless and stone is of finite density & some finite volume. Now only weight of stone will contribute in displacing certain volume of water. The proportion of density between water and pebble will decide how much volume (multiple of stone's volume) water will be displaced. As the weight of stone will be equal to the weight of displaced water I.e. Archimedes principle. Let's say the density of stone is 1000 times that of water. So when pebble is in the boat it will displace 1000 times more volume compared to the pebble sinking to the bottom of the pool. Because when pebble is sinking it is only displacing its own volume. So level of swimming pool will fall after throwing the pebble.