physics problem

[Phred]

Okay,

So you're in a rowboat in the middle of a lake. Inside the boat is an iron anchor - not attached to a rope.

You throw the anchor into the water and obviously it sinks to the bottom.

My question is this, at what point is the water level of the lake the highest (when measured against the shore, not the boat).

a) When the anchor is in the boat or
b) when it is in the water. Or,
c) are they both the same?

Note - I am Assuming that you could actually measure any minute difference in water level here. Also, this lake has no fish, or plants or mud or anything else to interfere with the measurement.

Note - I did give you enough information to solve this.
Phred

[lighthouse]

jajaja.....lots of free time he?
when the anchor is in the water (option b)
there`s a theory about it but I don`t know it`s name in english, in spanish would be: "el principio de Arquímedes"

anyway....


*Note: I`m supposed to be working!! :twisted:



Juan Pablo

[Taurus]

I believe when its in the boat, since then the boat will have more downforce cause of the weight, so if the boat is big and heavy enoguh, then it take its space of more water below it, and pushes it aside. THat will raise the waterlevel on the shore the most.

[Spacehog]

It would surely depend how heavy the anchor is relative to the boat... the natural buoyancy of the boat would counteract the weight of the anchor to some extent when it was *in* the boat... my logic would suggest the water would be infinitessibly higher when the anchor is in the water, not in the boat... but it'd have to be a very small diameter lake to make any measurable difference at all.

Martin

[Phred]

Some hints:




Hint 1.

When in the boat, the anchor would displace water based on its mass (weight).

Hint 2.

When in the water, the anchor would displace water based on its volume

Hint 3.

Density is Mass/Volume. The Density of water is 1 (mass = volume). Things that sink have a density greater than water.

Hint 4.

I said that the anchor sinks.



Does that help?

[Enigma™]

yup.

based on the density of the anchor and displacement value, without knowing the specific density/volume ratio, again it's still to hard to tell.

Assuming that the anchor weighs 5 pounds, but is only 2 inches cubed, it's going to displace more water IN the boat.

Change that around a bit though: If the anchor were 3 pounds, but took up 2 feet cubed *assuming that it's still dense enough to sink* then it's going to displace more water then it has ability to force the boat down with gravity to displace water.

Without knowing the specifics, I'd say that it's going to displace more water from IN the boat then out, but that's just what I think.

[Enigma™]

Ahhh I see now.

If it sinks then it's density is being "wasted" so to speak, so basically if it sinks, then it's going to displace more water from in the boat then out. :)

[jordanrudessjr]

i think the water level would be the same. I look at it like this way, if there was no anchor in the boat the water level would be higher then then if there was and if there is an anchor in the boat it has the same displacement as it does in the water because it is the same object. But i havent even taken physics yet so who knows.

-JRJR

[Phred]

Enigma you got it...

The trick is that the anchor sinks, so it will displace more by its mass than it's volume. (in other words since it sinks, M > V). Therefore the water level will be higher when the anchor is in the boat.

If we were talking about something the same density of water (like say... uh water...) then the water level would stay the same.

[Taurus]

THats odd. You mean if i fill my bathtube and put a 30cm3 plastic cube in it, the water rises less then when i put a 30cm3 cube made of LEAD in it?

Or perhaps a 30cm3 cube of thin extremely heavy lead, but totally filled with air on the inside...

:?:

[Compadre Moncho]

I think when it's on the boat... because... the water raise because of the water the boat displaces... so if it's on the boat it will make the boat displace more water volume that the volume the anchor displaces...
o
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o
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[The White Raven]

good problem phred.

i'm going to say it to my ohisics teacher if he can solve it.

[Phred]

THats odd. You mean if i fill my bathtube and put a 30cm3 plastic cube in it, the water rises less then when i put a 30cm3 cube made of LEAD in it?

Not quite. If you put these two cubes in the water as in submerged them, they would displace the same amount of water. Because inside the water the displace by volume and both have the same volume.

However, if you put them one at a time into a plastic boat, the lead cube will displace more water.

You could try something similar by taking a plastic boat into a sink. Put some weight in it and see how high the water is when the boat is just about to overflow. Now, with the same weight inside, let the boat overflow and sink to the bottom. Most likely you will see the water level go down.

[Enigma™]

exactly - it's mass displacement vs volume displacement. The volume displacement of the anchor is going to be the same no matter what the mass *provided it's more dense then water, otherwise it'd float* which is the volume issue solved: Underwater, the density is not going to displace any DIFFERENT amount of water. Density therefore underwater = moot.

HOWEVER in a boat, that is different. The boat would currently be a resisting force. Whatever. The point is that if the anchor sinks, then the density is higher then water. Period.
If you had a bucket of water, and you poured that bucket into the water, there's going to be no difference then if you had the bucket in the boat *suspecting you didn't consider the density of the bucket*
However, if you had a bucket of something heavier then water, the amount of water it's going to displace by the bouyancy of the boat is going to be more then the physical space it takes up.

Suppose it were opposite however:
Styrofoam. It floats, therefore it's density is less then water.
In this case, the volume is going to have more displacement value then the mass because the water is more dense.

And I'm tired. I'm going to bed now ;)

[Phred]

Enigma,

You rock. I have had fun with these brain things. My head hurts and I am done with thinking for a while.

Time to watch some tv... ;)

[Enigma™]

NOOO!! not the TV!!!!

Your IQ will drop faster then Britney Spears panties!!!

NOOOO!!!

*Tries to save Phred from the abuse that is Television*

[Taurus]

Hah! cool that means i was right in my first shot :P

\o/ \o/ \o/ \o/

*happy jump jump breaks his neck..*

[Ehren]

I think when it's on the boat... because... the water raise because of the water the boat displaces... so if it's on the boat it will make the boat displace more water volume that the volume the anchor displaces...
o
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o
!
-._!_.-

That picture has to be the highlight of this whole thread.

[WoofWoofX]

Ummmm... I guess there should be a 4th alternative... that is:

the moment +0 that comes directly after dropping the anchor in the water...

in this case you have the force of the dropp + the weight of the anchor (which density is greater then water) and that will create an impact wave at the time of the water contact... resulting a wave that will be higher then both other alternatives...

//WoofWoofX

[The Wizard]

Ummmm... I guess there should be a 4th alternative... that is:

the moment +0 that comes directly after dropping the anchor in the water...

in this case you have the force of the dropp + the weight of the anchor (which density is greater then water) and that will create an impact wave at the time of the water contact... resulting a wave that will be higher then both other alternatives...

//WoofWoofX

Yeah, that's an important observation.

[WoofWoofX]

Thank you (((Bowing in respect)))