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

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A floating block displaces water equal to its weight due to the principle of buoyancy, which states that the buoyant force (Fb) equals the weight of the object (W) when in equilibrium. In the case discussed, the block floats with half its volume submerged, leading to the conclusion that the buoyant force is W, not 1/2 W. The amount of submerged volume depends on the object's density relative to water, but if the block is floating, it must displace enough water to equal its weight. A block cannot float without displacing water, as it would contradict the principles of buoyancy. Thus, the buoyant force remains equal to the weight of the block regardless of how much volume is submerged.
get_physical
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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?
 
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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?
 
get_physical said:
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?
 
get_physical said:
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.
 
In other words, is Fb still W if the block floats ON the waterline? (without any volume of the block submerged)
 
get_physical said:
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.
 

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