Calculating Depth of Flat-Bottomed Barge in Freshwater

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Homework Help Overview

The problem involves calculating the depth of a flat-bottomed barge floating in freshwater, given its mass and dimensions. The context is centered around buoyancy and the relationship between the weight of the displaced water and the weight of the barge.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the principle of buoyancy, noting that the barge will sink until the buoyant force equals its weight. Questions arise about how to calculate the weight of the displaced water and the relationship between mass, density, and volume.

Discussion Status

Some participants have provided insights into the calculations needed, such as the relationship between the mass of the displaced water and the volume of the barge submerged. There is ongoing exploration of how to determine the depth of the barge below the waterline.

Contextual Notes

Participants are working with the assumption that the density of freshwater is known and that the barge's dimensions are fixed. There is a focus on understanding the principles of buoyancy without providing direct solutions.

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Homework Statement



A flat-bottomed barge, loaded with coal, has a mass of 3.0 105 kg. The barge is 20.0 m long and 9.8 m wide. It floats in freshwater. What is the depth of the barge below the waterline?
____ m

Homework Equations





The Attempt at a Solution



I have no idea which equations to use or even how to solve this problem. Any help would be awesome thanks!
 
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An object (the barge) will sink until the buoyant force upwards is equal to the weight of the object. The size of the buoyant force is equal to the weight of the water that is displaced by the barge. The volume of water that is displaced will be equal to the volume of the barge under water.
 
how do i find the weight of the water that is displaced by the barge?
 
Jtappan said:
how do i find the weight of the water that is displaced by the barge?

mass = density x volume
 
that is the mass of water that is displaced = density of water x volume of water?
 
Jtappan said:
how do i find the weight of the water that is displaced by the barge?

Jtappan said:
that is the mass of water that is displaced = density of water x volume of water?

yes, but remember the weight of the water will be equal to the weight of the barge. Also remember that volume = l x w x depth. You are looking for the depth
 
ahh i totally forgot about the l x w x h thing thanks!
 

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