Barge Buoyancy: Calculating Depth Change with Loaded Crate | Homework Help

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In summary, the conversation discusses a problem where a rectangular barge with dimensions of 5m by 2m floats in fresh water. A 400-kg crate is loaded onto the barge and it is asked to show that the barge floats 4cm deeper. The conversation discusses the use of Archimedes Principle and the need to consider volume when dealing with buoyancy. The final solution involves finding the mass of water that the barge must displace in order to stay afloat after the crate has been added.
  • #1
mogibb1
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Homework Statement



A rectangular barge, 5m long and 2m wide, floats in fresh water. Suppose that a 400-kg crate of auto parts is loaded onto the barge. Show that the barge floats 4cm deeper.

Homework Equations



Archimedes Principle
P=m/v

The Attempt at a Solution



I know that the area of the barge = 2(5)+2(2) = 14m
I know that the density of freshwater = 1000 kg/m3
Not real sure where to go from here.
 
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  • #2
Every time you see buoyancy you should think "volume".
 
  • #3
Ok, so this is what I believe to be the answer:

400kg * 10 (for gravity) = 4000 / 1000 kg/m3

= 4cm
 
  • #4
What you wrote doesn't make sense. Please put units everywhere.
 
  • #5
To make more sense, here are the units:

400 kg * 10 m/s2 = 4000 kg m/s2

4000 kg m/s2 / 1000 g = 4 cm

I now I need to work more on the units/conversions, but I would like to know if my
thinking is correct or not on this. Thank you.
 
  • #6
In case you have not noticed, it can't be right - you have seconds on the left, there is no miraculous way they can cancel out and left you with cm on the right. That's why I asked you add units, they often are a simple and sure way of telling you the answer must be wrong.

What mass of water must the barge displace to stay afloat after the crate has been added?
 
  • #7
I appreciate your help. I really don't have much in the way of a formula (unless Archimedes principle is it) to go by and I'm trying to figure this out. The 400kg crate will displace 400kg of the water, isn't that right?

If I take the 400kg crate and divide it by 1000kg/m^3 water I get 0.4m^3 is this in the ballpark?
 
Last edited:
  • #8
You are on the right track now.
 
  • #9
Sorry to be so much trouble, but I'm not good with word problems and having to figure out what to plug into an equation. Thank you very much for your time and assitance.
 

1. What is barge buoyancy?

Barge buoyancy refers to the ability of a barge or boat to float in water. It is a measure of the upward force exerted by the water on the barge, which keeps it afloat.

2. How is barge buoyancy calculated?

Barge buoyancy is calculated using Archimedes' principle, which states that the buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object. This can be determined by measuring the weight of the barge and the amount of water it displaces.

3. What factors affect barge buoyancy?

The main factors that affect barge buoyancy include the weight and shape of the barge, the density of the water, and any additional weight or cargo on board. The shape of the hull, as well as any air pockets or compartments, can also impact buoyancy.

4. How can barge buoyancy be increased?

Barge buoyancy can be increased by increasing the volume of the barge, either by adding flotation devices or increasing the size of the hull. The weight of the barge can also be reduced by removing excess cargo or using lighter materials in its construction.

5. Why is barge buoyancy important?

Barge buoyancy is important for ensuring the safety and stability of the barge while it is in the water. If a barge is not buoyant enough, it may sink or capsize, causing damage to the barge and potentially endangering the crew and any cargo on board.

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