Tube Buoyancy Question: How Much Force Is Needed?

[jackrabbit]

Suppose you had a hollow tube, closed at both ends. The tube weighs 10 pounds and would float in water.

Suppose also there is an empty container with a hole at the bottom. The tube is stuck through the hole so that half of it is in the tank and half is sticking out the bottom. Assume a water tight fit between the tube and the hole.

Now, fill the tank with water so that the water surface is a foot or two above the top of the tube.

How much force is necessary to pull the tube through the water and completely into the container? (Assume for the sake of argument that there is no friction between the tube and the sides of the hole). Is it (a) 10 pounds; (b) 10 pounds plus water pressure; (c) something less than 10 pounds because the top half of the tube is buoyant even though the bottom half is sticking out the bottom of the hole; or (c) something else?

 

[Doc Al]

What do you think?

 

[jackrabbit]

I don't know. My gut says it should be the full 10 pounds plus water pressure, but I am having trouble figuring out why it wouldn't be less given the buoyancy of the top half (perhaps less than 10 pounds for the tube but then add water pressure?).

 

[Doc Al]

I don't know. My gut says it should be the full 10 pounds plus water pressure, but I am having trouble figuring out why it wouldn't be less given the buoyancy of the top half (perhaps less than 10 pounds for the tube but then add water pressure?).

Your gut is correct. Buoyant force is the net force on the body due to the pressure of the surrounding fluid. Under 'normal' circumstances, the body is completely surrounded by fluid or is floating, thus the buoyant force is upward. But in a case like you describe, the net force from the fluid actually pushes down on the object.

 

[pmacias]

The force needed to pull the tube through the water and into the container would be (b) 10 pounds plus water pressure. This is because the weight of the tube (10 pounds) is being counteracted by the buoyant force of the water on the top half of the tube, but the bottom half of the tube is still exposed to the water pressure pushing down on it. In order to completely submerge the tube into the container, an additional force equal to the water pressure on the bottom half of the tube would be needed. This force would vary depending on the depth of the water and the density of the water.