Volume/Displacement Problem

  • Thread starter j_suder2
  • Start date
In summary, to determine how far a Mississippi river barge will sink into the water when loaded with 3000 tonnes of coal, you need to first find the area of the barge in contact with the water. Then, convert the weight of coal to kilograms and use this to find the volume of coal. Next, use the density of water to determine how much water will be displaced by the weight of coal. Finally, use the formula height x length x width = volume to find the height of the displacement, which will tell you how far the barge will sink into the water.
  • #1
j_suder2
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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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  • #2
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.
 
  • #3
Ok so I can find the volume of water, I'm still having trouble finding the height of the displacment,
Thanks
 
  • #4
Height*length*width = voulme.
 
  • #5
Thanks,
I just had the wrong conversion from tonnes to kg's
 

1. What is the difference between volume and displacement?

Volume refers to the amount of space occupied by an object, while displacement refers to the amount of water that is displaced when an object is placed in it. In other words, volume is a measurement of space, while displacement is a measurement of the amount of water an object pushes out of the way.

2. How do you calculate volume?

Volume is calculated by multiplying the length, width, and height of an object. For example, if a cube has a length of 5 cm, a width of 5 cm, and a height of 5 cm, its volume would be 5 x 5 x 5 = 125 cm³.

3. What is the formula for displacement?

The formula for displacement is V = m/ρ, where V represents the volume of the object, m is the mass of the object, and ρ is the density of the liquid in which the object is placed.

4. How does displacement help determine an object's density?

Displacement can be used to determine an object's density by comparing the volume of the object to the amount of water it displaces. The density of the object can then be calculated by dividing its mass by its volume.

5. Why is the volume/displacement problem important in science?

The volume/displacement problem is important in science because it helps us understand the relationships between an object's size, mass, and density. It is also frequently used in various experiments and calculations, such as in determining the buoyancy of an object or the density of a liquid.

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