Finding the Density of a Wooden Cube Submerged in Water

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To find the density of a wooden cube submerged in water, the buoyant force acting on it must equal the downward force applied. The cube, measuring 30.0 cm on each edge, has a volume of 0.027 m³, which leads to a buoyant force of 267.3 N when submerged. Given that a force of 54.0 N is required to push the cube down, the weight of the cube can be calculated by setting the downward force plus the weight equal to the buoyant force. This results in the weight of the cube being determined, allowing for the calculation of its density. The final density of the wood is found to be 800 kg/m³.
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"A solid wooden cube, 30.0cm on each edge, can be totally submerged in water if it is pushed downward with a force of 54.0N. What is the density of the wood?"

I know so far that the buoyant force would equal the 54N, but I don't know how to get the mass of the cube to determine the density. Can you help?
 
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So the cube completely submerges into water...

Downward Force + Weight = Buoyant Upward Force

Solve as per above...Show your work..
 
No, you don't know the bouyancy force is 54 N! How much would a cube of water, 30 cm on a side, weigh? That's the bouyancy force pushing the wood upward. The weight of the cube, plus the 54N pressing it down must equal that. Set up that equation and you can solve for the weight of the cube of wood.
 
Buoyant Force= Density of water x Volume of cube x g

Why the full volume of cube?...

Weight of cube = density of cube x Volume of cube x g

Can you solve further?
 
Ah...800kg/m^3! Thank you!
 

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