# What is the magnitude of buoyant force acting on the block?

A 0.5kg block of wood is floating in water. What is the magnitude of buoyant force acting on the block?

I know that Fb = (density)(g)(V)
The density of water is 1000kg/m3.
g = 9.8m/s

There is no way i can calculate the volume of the block with the given information. Also i know the water displaced equals the weight of the block.

What am i missing to get the buoyant force?

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How large does the buoyant force need to be if it has to exactly cancel the gravitational force acting on the block?

HallsofIvy
Homework Helper
The fact that the block is floating is crucial!

If the buoyant force has to cancel gravity then it would be

Fb = 1000 - (9.81*0.5)
=995.1
That looks wrong, i think i need the volume of the block

Doc Al
Mentor
If the buoyant force has to cancel gravity then it would be

Fb = 1000 - (9.81*0.5)
=995.1
That looks wrong, i think i need the volume of the block
That is wrong. Since the block is floating, the buoyant force does cancel gravity, which means Fb equals the force of gravity. But what are you doing subtracting the weight from the density of water??? (Since the units don't even match, such a subtraction has no physical meaning.)

You don't need the volume of the block. (Hint: It's easier than you think!)

OK here goes
Like you said, since the block is floating the buoyant force is equal to the density of the water - the weight of the block
Fb = 1000kg/m3 - 0.5kg
=999.5
That still looks wrong

Doc Al
Mentor
Like you said, since the block is floating the buoyant force is equal to the density of the water - the weight of the block
Reread what I wrote. I never said such a thing--in fact I said that such a calculation makes no sense!

That is true, Sorry i misunderstod it but i will go again from the basis of the principle. "Archimedes’ principle states that the buoyant force is equal to the weight of the fluid displaced" so i am now sayin the buoyant force is 0.5N
????? I am lost now if that is not the answer. please provide more guidance

Right, the buoyant force is equal to the weight of the fluid displaced.

What is the weight of the displaced fluid if the block is floating?

Hence, what is the buoyant force?

Note: 'weight' is not the same as 'mass'!

Doc Al
Mentor
That is true, Sorry i misunderstod it but i will go again from the basis of the principle. "Archimedes’ principle states that the buoyant force is equal to the weight of the fluid displaced" so i am now sayin the buoyant force is 0.5N
Actually, what you need here is not Archimedes' principle, but just the conditions for equilibrium. There are only two forces acting on the block:
its weight, acting down
the buoyant force, acting up​
These must balance, since the block is in equilibrium, so the buoyant force just equals the weight (not the mass) of the block. If the mass of the block is 0.5 kg, what's its weight?