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# This submarine question is driving me crazy watch

1. A submarine floats in the ocean with half of its volume submerged. Calculate the mass of water required in the ballast tank in order that it may float completely submerged. The total volume of the submarine is 1200m3. Someone help me work this out as I missed the lesson we covered this. Thanks
2. Some things about buoyancy and floating.

To float, the upthrust must equal the weight, ie forces balanced.

The upthrust on the object is equal to the weight of water displaced.

Hence for floating, since the upthrust must equal the weight of the submarine, and the weight of the water displaced is equal to weight of the submarine

In otherwords, if half the volume of the submarine is 600m³ then 600m³ of water is displaced and this is the volume of water which has the same mass as the submarine.

Can you do it from here?

Clue
Spoiler:
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If the submarine is fully submerged it is now displacing twice the volume of water so the upthrust is twice as big. You will have to increase the weight of the submarine to balance it.
3. (Original post by phys981)
Some things about buoyancy and floating.

To float, the upthrust must equal the weight, ie forces balanced.

The upthrust on the object is equal to the weight of water displaced.

Hence for floating, since the upthrust must equal the weight of the submarine, and the weight of the water displaced is equal to weight of the submarine

In otherwords, if half the volume of the submarine is 600m³ then 600m³ of water is displaced and this is the volume of water which has the same mass as the submarine.

Can you do it from here?

Clue
Spoiler:
Show

If the submarine is fully submerged it is now displacing twice the volume of water so the upthrust is twice as big. You will have to increase the weight of the submarine to balance it.

Okay i understand the displacement of water is equal to the volume of the submarine. But what correlation does that have with mass. Are there any equations. Also is the amount of water displaced equal to how much water is needed in the ballast tank? And if there is twice the upthrust when the sub is submerged fully, then does that mean you would have to double the volume of water displaced? And if so then would there need to be 2400m3 of water in the ballast tank? Thanks for the help
4. Weight = m x g

When the submarine is half submerged it floats and displaces 600m³ since this is half the volume of the submarine, so the weight of 600m³ of water is the upthrust and is equal to the weight of the submarine.
So find the mass and therefore the weight of 600m³ of wateer, this must be the weight of the submarine.

When the submarine is fully submerged, it has displaced 1200m³ of water, since this is the total volume of the submarine.
Calculate the mass and therefore the weight of the 1200m³ of water, that's the upthrust.

You already know from the first part of the questions what the weight of the submarine is. How much MORE weight do you need to add to it to make it equal to the new upthrust? This is how much water you need to add.
5. (Original post by phys981)
Weight = m x g

When the submarine is half submerged it floats and displaces 600m³ since this is half the volume of the submarine, so the weight of 600m³ of water is the upthrust and is equal to the weight of the submarine.
So find the mass and therefore the weight of 600m³ of wateer, this must be the weight of the submarine.

When the submarine is fully submerged, it has displaced 1200m³ of water, since this is the total volume of the submarine.
Calculate the mass and therefore the weight of the 1200m³ of water, that's the upthrust.

You already know from the first part of the questions what the weight of the submarine is. How much MORE weight do you need to add to it to make it equal to the new upthrust? This is how much water you need to add.
Oh right so i just had to convert 1200m3 of water into mass? Using the equation P x volume=mass and assuming pressure of water is equal to 1030 kg/m3. I multipied 1030 by 1200 and got 1236000kg as my answer. Is this correct?

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