Calculating Depth of Flat-Bottomed Barge in Freshwater

[Jtappan]

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!

 

[Galileo's Ghost]

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.

 

[Jtappan]

how do i find the weight of the water that is displaced by the barge?

 

[Galileo's Ghost]

how do i find the weight of the water that is displaced by the barge?

mass = density x volume

 

[Jtappan]

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

 

[Galileo's Ghost]

how do i find the weight of the water that is displaced by the barge?

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

 

[Jtappan]

ahh i totally forgot about the l x w x h thing thanks!