# Ship's mass/displacement, buoyancy

1. Oct 17, 2009

### Hippoman

Ok, so I've a couple of assignments that require the understanding of the basic principles of buoyancy and displacement of a ship and I'm a bit confused.

Consider a ship that has a displacement of 7 000 000 kg. That's the mass of the water that the ships displacement "pushes out" from its way, right? So why is it generally stated that displacement = mass of the ship (for example Wikipedia states this)?

If the buoyancy force acting on the ship = water density * g * displacement volume.
Now if we solve for the volume, we have a displacement volume (water density 1000kg/m3)
of 7000m3. Now, if we assume that the ship and the displacement are "fully wooden", so no empty spaces, the mass is 7000m3 * wood density, say 700kg/m3, = 4 900 000kg. So what's wrong here?

Generally speaking, is the displacement of a ship always the same? I mean, it cannot always be just the same amount of water that it's displacing because the ship has to go up an down from time to time. Why are the size of the ships demonstrated by the displacement if this is the case?

The other thing about the buoyancy: if we have an object laying at the bottom of the sea, is there a buoyancy force acting on it? I can't find any clear statement about this.

I realize that these should be easy subjects but I'm quite poor with physics so don't be too rough on me :)

2. Oct 17, 2009

### Staff: Mentor

This is Archimedes's principle. Assuming the ship is floating, the upward buoyant force equals the weight of displaced fluid and balances the downward weight of the ship.

The volume of the ship does not equal the volume of displaced water--it is greater.

I'm not sure what you're asking here.

It depends on how the object is in contact with the bottom. If the object is stuck in mud (for example) so that the seal is water-tight, then the net force from the surrounding water actually presses the object into the bottom.

3. Oct 17, 2009

### Hippoman

Ok, so basically what I want to know is this. If there's stated that a displacement of a certain ship is 9000 tons, can I take it so that the ship's mass is 9000 tons?

Clarifying the third question: For example Titanic had a displacement of 52,310 tons (http://en.wikipedia.org/wiki/RMS_Titanic). What if you add weight to the ship, the displacement has to change, right? Isn't that quite an inconvenient way of expressing the size of a ship, since you can't really know how much weight it carries from time to time?

4. Oct 17, 2009

### Staff: Mentor

Yes. (But see the link below.)

Of course: the literal displacement will increase if weight is added. But it depends on what displacement they are quoting. Is it the fully-loaded displacement? See: http://en.wikipedia.org/wiki/Displacement_(ship)" [Broken]
Not necessarily.

Last edited by a moderator: May 4, 2017