Why Does a Floating Block Displace Water Equal to Its Weight?

[get_physical]

the problem is:
a block that weighs W floats exactly with 1/2 of its volume below the waterline. What is the buoyant force?

Answer is W, but why is it W?

I thought that its 1/2 W because only 1/2 of the volume is below the waterline. if the buoyant force equals to the downward force, wouldn't the block be floating ON the waterline?

 

[get_physical]

By reading a few other posts on this forum, I think that I understand this to be an equilibrium concept in which if it is floating, then the Fb = to the weight of the block. However, what would the Fb be if the block was floating in the waterline?

 

[Doc Al]

By reading a few other posts on this forum, I think that I understand this to be an equilibrium concept in which if it is floating, then the Fb = to the weight of the block.

Right.

However, what would the Fb be if the block was floating in the waterline?

What do you mean? If it's floating, and the only forces acting are gravity and the buoyant force--what can you conclude?

 

[Doc Al]

I thought that its 1/2 W because only 1/2 of the volume is below the waterline. if the buoyant force equals to the downward force, wouldn't the block be floating ON the waterline?

If something is floating, then the buoyant force equals the object's weight. That's that!

But how much of the object is under water is a different question. That depends on how the density of the object compares to the density of water.

 

[get_physical]

In other words, is Fb still W if the block floats ON the waterline? (without any volume of the block submerged)

 

[Doc Al]

In other words, is Fb still W if the block floats ON the waterline? (without any volume of the block submerged)

That's not physically possible. If the object has weight it must displace some water.