Calculating Buoyancy and Weight in a Sinking Ship Diorama

[nbontra]

I'm constructing a diorama of a ship sinking, and I haven't been able to find any details on the physics behind it. I'm an art student, so my knowledge in physics is limited to what I read here and in a few books at home.

I'll most likely construct a fish tank that is 4'x1'x1' to contain the water and toy ship. My question is to what formula I would use to determine how heavy to make the toy ship. Is it just a scale issue? Where I could just use the size ratio to figure out the weight? If I go that route, will the amount of water or the size of the tank affect the rate at which it sinks?

Also, I'll be using an air compressor hose to attempt to raise the ship while it is sinking. How does one determine how much air can raise a certain amount of weight underwater?

Thanks!

 

[mgb_phys]

It depends on the volume and mass of the ship. Unless it is a very simple crude shape it is going to be difficult to calculate the volume of the ship.
To measure the volume fill a container to the top with water, push the model under the water and cathc the extra water that overlfows. The volume of this water is the displacement.
Fresh (ie not salt) water weighs 1Kg / litre so your boat has to weigh more than 1Kg for each litre it displaces.
You will probably have to add weights to make it sink.

Then to make it float again you add air from the hose. For every litre of air you add you get 1kg of lift.

With a detailed model you are also going to have problems with air bubbles caught in small details.
You are probabaly ging to have to experiment to get it right.

 

[Loren Booda]

Viscous effects, those which influence the resistance of the ship to the water, are related to the surface area of the ship exposed to the water, and determine a terminal velocity for the sinking ship. Buoyancy, or lack of it, determines the acceleration component of sinking, and is related to the density of the ship minus the density of water displaced by it, as mgb_phys mentioned. Take care to consider (or eliminate) any air bubbles, also using Archimedes' principle! A simple shape that you may want to experiment with is that of a submarine rather than a ship.

 

[nbontra]

thanks for the info, i surely appreciate it!