[ironic it's me] Physics/philosophy question, thoughts and explanations needed

[pi]

Out of curiosity, what's your thoughts on this:

"if you are in a boat in a lake and throw a stone out of the boat, what happens to the level of the water?"

I don't know the answer btw.

[kenhung123]

Are you asking whether the water splashed out is more than the volume increase from the stone entering?

[pi]

I got the question from another site (so I could be wrong), but my understanding was that it was asking whether or not the water-level of the lake (I'm assuming this is not in relation to the boat, but in relation to the "shore" or something) rose after the rock was submerged following it being thrown by you from the boat. I'm assuming all the splashed water went back into the lake in it's entirety.

Not sure if that clarifies it :/



Found the answer for those interested, but have a go first yourself!

Spoiler

Credit: http://answers.yahoo.com/question/index?qid=20061203031452AAuD4k2

 The water level goes DOWN. (siddarth had the right answer, but the wrong reason ... he is ignoring the fact that everybody else is raising, namely that the stone still displaces some water ... my point is that it displaces less water.)

When something floats, it displaces its *weight* in water.
When something sinks, it displaces its *volume* in water.

So while in the boat, the weight of the stone displaces a lot of water. But when tossed in the lake, it displaces a small amount of water. So the level of the lake would drop slightly.

To see this more clearly, imagine that you have some ultra-dense rock so that something the size of a golf ball weight 500 pounds. While in the boat, this contributes 500 pounds to the weight of the boat and so the boat (with the golf ball) displaces 500 pounds worth of water. That's a lot of water.

But when you drop the golf ball in the lake, it displaces an amount of water the same volume as the golf ball ... which is not very much. Meanwhile the boat just got 500 pounds lighter, and is thus displacing 500 pounds less water. So the level of the water goes down.

So what if the reverse were true, and the 'stone' was made of some ultra-light material so that something the size of a basketball weighed only 1 gram? In that case it would float, and would make no difference if it was inside or outside the boat.

But since we're talking about a stone ... something assumed to be denser than water (which means that its weight in water exceeds its volume in water) ... the water level would drop.

[golden]

I haven't read the above, so I could just be reiterating something in less detail.
Think of it this way:
When it's in the boat, it's supported by the force due to the water.
When it's off the boat, it's supported by the force of due to the water, but this force is not as great, otherwise the rock wouldn't be sinking.
Because the buoyant force depends on the mass of water displaced, therefore when it's on the boat, the mass of water displaced is larger.
Because the mass of water displaced is larger, the water level is higher.

If you need any elaborations then I'd be happy to provide them.

[Aurelian]

Hmmmm the easiest way to understand this is just using Archimedes' principle and basic fluid physics.

Assume we have a massless tub in which we put the rock. We then place the tub on the water surface, and since it floads Archimedes' principle will state that the weight of the water displaced will equal the weight of the rock. We will call this situation A.

When we remove the rock and drop it into the water, since it sinks we know that the buoyancy force acting on the rock must be less than the weight force of the rock. The buoyancy force equals the weight of water displaced by the rock, and the volume of this water is just the volume of the rock. Let's call this Situation B.

What this means is that the mass of water displaced in Situation B must be less than the mass of water displaced in Situation A because now the water displaced is only supporting some of the weight of the rock.

If less water is displaced, then the water level must be lower.

Not sure why this would be a 'philosophy' question

EDIT: See http://en.wikipedia.org/wiki/Archimedes'_principle if you're wondering where this type of reasoning comes from.

[availn]

Not sure why this would be a 'philosophy' question

Otherwise it would be a 100% physics question, and we can't have that, can we?