Calculating Depth of Flat-Bottomed Barge in Freshwater

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In summary, a flat-bottomed barge, loaded with coal, has a mass of 3.0 105 kg and is 20.0 m long and 9.8 m wide. It floats in freshwater. To find the depth of the barge below the waterline, you need to use the equation weight = density x volume. The weight of the water that is displaced by the barge will be equal to the weight of the barge itself. The volume of water displaced will be equal to the volume of the barge under water, which can be found using the equation volume = length x width x depth. Thus, by rearranging the equation, you can find the depth of the barge below the water
  • #1
Jtappan
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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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  • #2
An object (the barge) will sink until the bouyant force upwards is equal to the weight of the object. The size of the bouyant 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.
 
  • #3
how do i find the weight of the water that is displaced by the barge?
 
  • #4
Jtappan said:
how do i find the weight of the water that is displaced by the barge?

mass = density x volume
 
  • #5
that is the mass of water that is displaced = density of water x volume of water?
 
  • #6
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
 
  • #7
ahh i totally forgot about the l x w x h thing thanks!
 

1. How do you calculate the depth of a flat-bottomed barge in freshwater?

To calculate the depth of a flat-bottomed barge in freshwater, you will need to know the dimensions of the barge, including its length, width, and draft. The formula for calculating depth is draft = displacement / (length x width), where displacement is the weight of the barge in freshwater. This formula assumes that the barge is floating evenly on the water.

2. What is the displacement of a barge in freshwater?

The displacement of a barge in freshwater is the weight of the barge when it is fully submerged in freshwater. This weight is equal to the weight of the barge itself, plus the weight of any cargo, passengers, or equipment on board.

3. Is the calculation for depth of a barge different for different sizes or types of barges?

The calculation for depth of a barge is the same for all sizes and types of flat-bottomed barges in freshwater. However, the dimensions and displacement of the barge will vary, so the specific numbers used in the calculation will be different.

4. How accurate is the calculated depth of a barge in freshwater?

The accuracy of the calculated depth of a barge in freshwater will depend on the accuracy of the measurements used in the calculation. If the dimensions and displacement are measured precisely, the calculated depth should be accurate. However, other factors such as uneven loading or water density variations can affect the actual depth of the barge.

5. Can this calculation be used for other types of vessels besides flat-bottomed barges?

The formula for calculating depth of a barge in freshwater is specifically for flat-bottomed barges. Other types of vessels, such as ships with different hull designs, may require different calculations to determine their depth. It is important to use the appropriate formula for each type of vessel to ensure accuracy.

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