How Deep Does a Barge Sink with 3000 Tonnes of Coal?

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To determine how deep a Mississippi river barge sinks when loaded with 3000 tonnes of coal, the area of the barge in contact with water is calculated first. The weight of the coal is converted from tonnes to kilograms, facilitating the calculation of the volume of water displaced. The relationship between the weight of the coal and the volume of water displaced is established using the density of water, which is 1000 kg/m^3. The final step involves calculating the height of water displacement using the formula for volume, which is height multiplied by length and width of the barge. The discussion highlights the importance of accurate unit conversion for successful calculations.
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Homework Statement


A Mississippi river barge is 65m long and 20m wide. How far will it sink into the water when 3000 tonnes of coal is placed on it?


Homework Equations


rho=m/v, L x W = A,


The Attempt at a Solution



I figured out the area of the barge in contact with the water, then converted the tonnes to kilograms. I used this to get the volume of coal taken off. (I think that works).
I guess from here I need to use the density of water to see how much is displaced by that amount of coal, and then determine the height of water this would correspond to.
I'm stuck at this last part.
 
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Weight of water displaced = weight of coal, which means,
Volume displaced of water (not coal) X density of water = weight of coal.

Density of water can be taken to be 1000 kg/m^3.
 
Ok so I can find the volume of water, I'm still having trouble finding the height of the displacment,
Thanks
 
Height*length*width = voulme.
 
Thanks,
I just had the wrong conversion from tonnes to kg's
 
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