Some Physics Problems: Fluids

[biggsauce]

Heres the scenario:

There is a swimming pool with a boat in it. In the boat is an anchor. The boat is roughly the size of the pool, and the pool is roughly the shape of the boat.

Lets say you take the anchor out of the boat and put it on the ground. In this case, the water level will lower relative to the sides of the pool.

Now, instead of putting the anchor on the ground, you put the anchor in the water. I would say that the overall water level wouldn't change because although the water level lowes when the anchor is removed from the boat, it will displace water again and raise the water level back to where is was when the anchor was in the boat.

This was a homework problem that I had a few weeks ago and its been bugging the hell out of me, because I got it wrong. The right answer is the water level lowers. A buddy of mine said its because the anchor doesn't displace water when it is in the water. Yeah, ok man .

Anyone have any ideas? Would the weight of the anchor cause the boat to displace more water than if the anchor were in the water by itself? I guess this would make sense for a very dense anchor, but what about an anchor with a density closer to that of water?

[Fnord]

After a brief experiment, it depends on the density of the anchor.

When the anchor is in the boat, it displaces an amount of water equal to its mass. When its in the water, it displaces an amount of water equal to its volume.

If the anchor is (hypothetically) the same density as water, there will be no rise or fall.

[psycix]

When the anchor rests on the bottom of the pool, this weight is substracted from the boat.
The boat will float higher, and thus displace less water, dropping the water level.

[biggsauce]

When the anchor rests on the bottom of the pool, this weight is substracted from the boat.
The boat will float higher, and thus displace less water, dropping the water level.

Read more into how _fnord put it, I like his wording better than my own
Becasue the anchor has volume, it has to displace water. I had someone actually try to convince me that the anchor essentially didn't have volume. Seriously, wtf.

Imagine an anchor with next to no mass (like a hollow shell) that was held underwater somehow. When it is taken out of the boat, there will hardly be a difference in the water level, but when it is submerged, the water level will rise an equivalent amount to the anchor's volume.

The question does't deal with specific masses, so I was beginning to think it is a poorly constructed question.

Thanks _Fnord, you put it in much better terms hat what I was thinking.

[boilingleadbath]

Density of the anchor is irrelevant.
Volume of the anchor is irrelevant.

The boat (which, in our analysis, includes anchor; the anchor is part of the "boat"), if the downwards force is constant, must always displace a certain quantity of water.

If you lower the anchor into the water, the downwards force on the system doesn't change. (ignore the gradient in the gravitational field, it's ~10E-6 at most) The boat-anchor system has changed shape, but this is buoyancy and so the shape doesn't matter.

If you lower the anchor into the water <i>and it touches the bottom</i>, the "net" (ignoring buoyant force) downwards force on the system does change... because the ground is now pushing upwards on the anchor. Thus boat-system displaces less water. Thus water level drops.

*****

If the question read "you lower the anchor into the water", I'd complain about the semantics of the question... loudly in class.

If the question read "you lower the anchor into the pool", I'd grumble about the poorly worded question.

My instructors often find my attention to accuracy annoying.

[ALIHISGREAT]

quite a nasty question... i can't understand why your teacher didn't give you the correct answer? and i agree its a poorly worded question...

i like the way _Fnord and BLB worded their answers but i couldn't tell you which is right.... maybe a cross breed of both?

[psycix]

Agree with boilingleadbath.
Just like I stated, the weight of the anchor is not anymore resting on the boat.
The density doesnt really matter, its higher then that of the water anyway (or else it wouldnt sink) and the actual weight doesnt make the difference of raising and lowering the water level.

[jook13]

the way I see it, when the boat has no anchor, it will have the same amount floating above water no matter what is thrown into the pool. as the water rises, so will the boat. So basically if you remove the anchor, the boat will rise. then if you throw the anchor in the pool, the water level will rise. then the boat will rise with the water. (unless I missed a part of the question)

[biggsauce]

Ok basically the question is asking what the water level would do the anchor was removed from the boat. (boilingleadbath brought up a great point on whether the anchor is suspended in water from the boat or is allowd to sink to the bottom) Whether the water level drops or stays the same depends on that factor, which the question doesn't say specifically.