Finding the Density of a Wooden Cube Submerged in Water

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Homework Help Overview

The problem involves determining the density of a wooden cube that is submerged in water, given its dimensions and the force required to keep it submerged. The subject area pertains to fluid mechanics and buoyancy principles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the forces acting on the cube, including buoyant force, weight, and the applied downward force. There are attempts to set up equations based on these relationships and to clarify the concepts of buoyancy and weight.

Discussion Status

Some participants have provided guidance on how to relate the forces involved, while others have questioned assumptions about the buoyant force and its calculation. Multiple interpretations of the problem setup are being explored, and there is an ongoing exchange of ideas without a clear consensus.

Contextual Notes

The discussion includes considerations about the weight of the water displaced by the cube and the need to calculate the weight of the wooden cube to find its density. There is an implicit understanding of the constraints of the problem based on the information provided.

psycovic23
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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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