archimedes question

[scottyT]

I found this in a PR book.

A sailboat is anchored in an enclosed pool. When the anchor is pulled off the bottom of the pool and into the boat:

A- the water level stays constant and buoyant force on the boat increases.
B- the water level rises and buoyant force on the boat increases
C- blah ... "blah blah"
D- blah? blah, blah!


My reasoning is that the answer is A. The buoyant force will clearly go up because displaces more fluid with an anchor on board. I'm picturing that the anchor displaces 1 anchor-volume of fluid on the bottom of the pool so the water level shouldn't change as it's brought into the boat. Sure the boat will sink a little bit but that water has already been displaced from the anchor being at the bottom .......... hmm, maybe I just answered my own question. I guess if you bring in an extremely dense anchor onto the boat you increase the average density of the boat and it can displace more volume as a boat-anchor system than separately. Any thoughts?

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[physics junkie]

I'll come up with an extreme example using neutron star material(most dense stuff I know of). Imagine a piece of neutron star material. Let's say it's 1000kg and 1mm^3 in volume. This is actually a gross understatement as a spoonful of neutron star material would weigh as much as Everest. It's not going to take up a whole lot of space in the water if its your anchor. Yet, if you pull it up and onto your boat, it's going to push your boat a few feet above its usual water line...thereby displacing more water in the boat than it could in the water.

To put it in physics terms: In the water the anchor obviously displaces a volume of water equal to the volume of the anchor. In the boat the anchor weighs the boat down which will result in the anchor effectively displacing a volume of water that would weigh as much as the anchor.

So the answer is B.

The the water line stays the same is if the anchor has the same density as water. Can you reason what would happen if you had an object with a density 1/3 that of water in the boat and then tossed it in the water? How would the water level in the lake change?

It's sad that Kaplan has resorted to passing off well known brainteasers(I was first asked this in elementary school as a question of the week) as MCAT physics prep.

 

[BloodySurgeon]

I could be wrong but this is my interpretation of the question: what will happen if you add more weight onto the boat. If the anchor is brought up from the floor of the ocean onto the boat thats more weight added. If mg is increasing then the buoyant force will also increase. Now if the buoyant force increases, the density of water and acceleration of gravity is constant, then the volume of displaced water increases. And as you know with archimedes famous naked bath run, if you step into a full bathtub then the water will overflow with the same amount of volume displaced. Eureka!

 

[scottyT]

My original thought was that the total buoyant force would be the same for the whole system but I see now that the total buoyant force goes up when the anchor is hauled on board because it can effectively displace more water on a ship than on the bottom.

I guess the only situation where the volume of the pool wouldn't change would be if you were bringing water or something of equal density on board (from the pool). The boat would sink, buoyant force would go up and the pool would rise ... but only by the amount of water that you put on the boat (I think). Anyways it's neat to think about.

Thanks for the help to both of you.