Test your buoyancy understanding!

[windapp]

I think you have that backwards, the aluminum is a greater volume and will cause a greater change

The aluminum will take up more volume when sunk, and exactly the same volume as the lead when floating (The canoe actually takes up the additional volume produced by the weight).

I don't have it backward. More volume when sunk = less change. In fact look at the case of a neutrally buoyant object. In this case, there would be absolutely no change because it takes up the same volume whether floating or sunk.

 

[dpaustex]

Folks, the water level stays exactly the same, if both items are in equilibrium.

Regardless of what's in the canoe in the first example, the water displaced in the pool is equal to the upward buoyant force. In equilibrium (canoe not bouncing, etc), the weight of the displaced water, that the canoe "pushes down", is exactly equal to what the canoe, and everything in it, weighs. This equates to the overall "level" of the pool.

Similarly, the same rock, over the edge, still displaces the same "weight" of water. The canoe displaces it's own weight, too. While the stone "feels" lighter, to a person holding the rope tied to it in the canoe, the weight of displaced water is the same.

If you draw an equilibrium force diagram, you will see this is true.

(I cheated, I'm a structural engineer).

 

[windapp]

i agree 100 % and that is the answer to the original post. the answer that it will remain the same iss only correct if the displacement of the rock is same weight as the rock. and that is not the case so when the rock is tossed overboard the water level will drop. in other words a 50 lb one gallon rock in a boat displaces 50 lbs while in the boat. it displaces 8 lbs in the water, allowing the water level to drop when thrown overboard. its kind of the same as what weighs more , a lb of lead or feathers. with bouyancy it is what displaces more, a container of lead or a container of feathers. and it is neither it is the container displacement.

And I did check the weight of 1 cu ft of water to ensure it wasn't a trick question.

 

[The Chairman]

Lets show how the water level in the pool will decrease mathematically. Consider a cubic foot of lead which weights 709 pounds. In order for it to be neutral, it would have to have a volume of 11.44 cubic feet. 709/62=11.44ft³. However, it's solid with no cavity to effect this it. Ergo, when the lead is placed in the canoe, it must displace 11.44 ft³ of water to remain floating. In fact, the canoe displaces 10.44 ft³ more water in the pool, then if it were NOT supporting the single cubic foot of lead and it was at the bottom of the pool. It doesn't matter if the lead is dry or in the water, as long as it's not touching the bottom, it will have to displace 11.44 ft³ of water in order tor the canoe to remain floating.

 

[NAM001]

and when the 1 cu ft of lead is put in water it removes the 11.44 from the boat and dispalces 1.0 in the water resulting is 10.44 less displacement in the pool when the lead is tossed over the side. whe water level goes down.

 

[The Chairman]

and when the 1 cu ft of lead is put in water it removes the 11.44 from the boat and dispalces 1.0 in the water resulting is 10.44 less displacement in the pool when the lead is tossed over the side. whe water level goes down.

Precisely. The canoe displaces less water allowing the outside water to go down.

 

[windapp]

Lets show how the water level in the pool will decrease mathematically. Consider a cubic foot of lead which weights 709 pounds. In order for it to be neutral, it would have to have a volume of 11.44 cubic feet. 709/62=11.44ft³. However, it's solid with no cavity to effect this it. Ergo, when the lead is placed in the canoe, it must displace 11.44 ft³ of water to remain floating. In fact, the canoe displaces 10.44 ft³ more water in the pool, then if it were NOT supporting the single cubic foot of lead and it was at the bottom of the pool. It doesn't matter if the lead is dry or in the water, as long as it's not touching the bottom, it will have to displace 11.44 ft³ of water in order tor the canoe to remain floating.

A cubic foot of lead weighs 409 lb.

 

[The Chairman]

A cubic foot of lead weighs 409 lb.

I'm talking about African lead, not European.

Density of metals

 

[windapp]

I'm talking about African lead, not European.

Density of metals

You are right. Re-did the calculation. Not sure what I did wrong in the first place.

 

[NAM001]

i believe you are right so long as the weight is attached to the boat by a rope. cut the rope and the things change, because the excess neg bouyancy is not transfered to the boat. cant comment on the force diagram, however no rope was in the example . as it is throw the weight ovverboard and the pool level will drop. your answer is correect for your example but not the one given.