Quick Puzzle...

[Woodchuck2000]

A fisherman sits in a boat in a mountain pool, with no flow out of it. He has a brick in the boat which he throws overboard. Does the level of the water rise, stay the same or fall, and why?
I think I've got an answer but any input is appreciated.

 

[Heisenberg]

Rises. The brick displaces some of the water.

Edit: I missed the part about the brick being in the boat to start with. Gonna have to think about it.

 

[Electric Amish]

On first instinct, it's gotta be rise, but the amount is probably immeasurable, depending on the volume of the lake.

On the other hand, the extra weight in the boat is already displacing water, so changing the location of the brick from the boat to the lake *probably* would cause it to stay the same.

amish

 

[Wallydraigle]

Stays the same. The brick's volume was already displaced when it caused the boat to ride lower in the water.

 

[Argo]

Stays the same. Since the displacement of the brick will be counteracted by decreased displacement of the boat, since it now weighs less by the weight of one brick. Hope this makes sense.

 

[rgwalt]

EDIT AGAIN:

For those saying that the water line will stay the same, once the brick is dropped overboard the boat will displace less water to balance the weight of the boat, and thus the water line on the side of the boat will fall. I understand the claim that the brick displaces a certain amount of water no matter if it is in the boat or not. However, when you throw the brick overboard, the whole level of the lake will rise, and the boat will rise along with it. Therefore, the boat will ride higher in the water, and the level of the lake will rise (only slightly)

Ryan

 

[notfred]

Well, the density of the boat decreases, so it sits higher in the water, lowering the water level. But, the volume of the brick underwater raises the water level.

However, the brick is more dense than the boat with a brick in it (as it sinks and the boat floated) so the volume displaced by the brick in the water is less than the volume displaced by the brick in the boat, so the water level falls.

 

[SammyBoy]

same

 

[Demon-Xanth]

Falls.

Inside the boat it's displacing it's weight in water, outside it's only displacing it's volume. (which is less)

 

[Woodchuck2000]

Originally posted by: Argo
Stays the same. Since the displacement of the brick will be counteracted by decreased displacement of the boat, since it now weighs less by the weight of one brick. Hope this makes sense.

Woah, that was quick

It's the level of the water relative to the shore that I'm concerned with.
My argument is that different conditions apply for bricks with densities <= water compared to bricks with densities > water.
If a 'light' brick is in the boat, the boat displaces water equal to the mass of the boat + mass of the brick. When the brick is chucked overboard, the boat displaces water of equal mass to the boat and the brick displaces water of equal mass to the brick. The water level stays the same,
If a 'heavy' brick is in the boat, the boat displaces water equal to the mass of the boat + mass of the brick. When the brick is chucked, it displaces less than it's own mass - it sinks, displacing a <volume> of water equal to its own. The boat's still displaces its own mass in water but the total displacement decreases so the level goes down.

Does that make sense or am I talking boll*cks?

 

[zsouthboy]

falls

 

[Argo]

Giving it more thought it depends on the density of the brick. The amount of water displaced by the brick while it's in the boat equals volume of water that weighs the same as the brick. Amount of water displaced while the brick sinks equals to the volume of the brick. Now it all depends on the density of the brick. If it's higher than that of water - level decrease. Lower or equal - it'll stay the same, since the brick will still displace the amount of water equal to it's weight.

 

[Woodchuck2000]

Originally posted by: Demon-Xanth
Falls.

Inside the boat it's displacing it's weight in water, outside it's only displacing it's volume. (which is less)

Ah, you posted that as I was typing... I think that's correct, assuming the brick has a density greater than water.

 

[notfred]

Originally posted by: Woodchuck2000

Originally posted by: Argo
Stays the same. Since the displacement of the brick will be counteracted by decreased displacement of the boat, since it now weighs less by the weight of one brick. Hope this makes sense.

Woah, that was quick

It's the level of the water relative to the shore that I'm concerned with.
My argument is that different conditions apply for bricks with densities <= water compared to bricks with densities > water.
If a 'light' brick is in the boat, the boat displaces water equal to the mass of the boat + mass of the brick. When the brick is chucked overboard, the boat displaces water of equal mass to the boat and the brick displaces water of equal mass to the brick. The water level stays the same,
If a 'heavy' brick is in the boat, the boat displaces water equal to the mass of the boat + mass of the brick. When the brick is chucked, it displaces less than it's own mass - it sinks, displacing a <volume> of water equal to its own. The boat's still displaces its own mass in water but the total displacement decreases so the level goes down.

Does that make sense or am I talking boll*cks?

Yes, that's what I said. If the brick is more dense than water, the level will go down.

 

[911paramedic]

Originally posted by: lirion
Stays the same. The brick's volume was already displaced when it caused the boat to ride lower in the water.

Yup.

 

[CTho9305]

Originally posted by: 911paramedic

Originally posted by: lirion
Stays the same. The brick's volume was already displaced when it caused the boat to ride lower in the water.

Yup.

No. In the boat, it displaced its weight worth of water. It is denser than water, so this is more than the brick's volume worth. When you drop it in the lake, it only displaces its volume worth, which is less, so the level of the lake falls. You can probably test this with a cup/bowl of water, a paper "board", and some coins.

 

[royaldank]

I'm voting it says the same.

BTW: When will you know the actual answer?

 

[herme5]

The water level drops. If it is assumed that the brick sinks, then the water level drops. The displacement of water is more with bouyancy is taken into the equation. Think of a log that floats... if it floats it would displace more water than if you were to decrease the size and increase the density (to make it sink).
In the same way, the boat acts as the floating object.... As long as it floats above the water it displaces more than if it sunk. The brick adds to the amount being displaced. Once dropped out of the boat, it becomes a object that only displaces by volume of a dense object.
It is a tricky question, but fun. Thanks.

 

[herme5]

The above answer is correct, too. I am positive of that.

 

[Jzero]

Throwing bricks into lakes is bad for the wildlife, therefore this question should be stricken from the record.

 

[Hanpan]

As am I

 

[Spyro]

Originally posted by: Jzero
Throwing bricks into lakes is bad for the wildlife, therefore this question should be stricken from the record.

Seriously though, this is (was?) a pretty neat puzzle

 

[Woodchuck2000]

Originally posted by: royaldank
I'm voting it says the same.

BTW: When will you know the actual answer?

I'm not entirely sure.... It was on a hydrostatics problem sheet and I don't know when its being marked.
Thanks for all the responses guys, I got my brain in a twist trying to figure it out and it's handy to bounce ideas off people.

 

[911paramedic]

Originally posted by: CTho9305

Originally posted by: 911paramedic

Originally posted by: lirion
Stays the same. The brick's volume was already displaced when it caused the boat to ride lower in the water.

Yup.

No. In the boat, it displaced its weight worth of water. It is denser than water, so this is more than the brick's volume worth. When you drop it in the lake, it only displaces its volume worth, which is less, so the level of the lake falls. You can probably test this with a cup/bowl of water, a paper "board", and some coins.

You are right, I didn't think about this very long. In order to recover a cubic foot of lead from the bottom of a lake with a float, it would take many cubic feet of air to raise it (cubic foot of water is ~65lbs I think). If it were sitting in a boat, it would displace the amount of water needed to buoy it. It comes down to a density factor.

 

[dighn]

drop

originally, the weight of water displaced is the same weight as the brick. water is lighter than bricks (lower density to be exact) so the volume is greater than the volume of the brick.

now you drop in the brick, the volume of water displaced is less.