Buoyancy and Density and Buoyancy

[xieon]

To start off, the problem. We had to construct a boat out of a 12''x12'' piece of aluminum foil. The purpose was to see who could estimate the closest number of cubes that could go inside the boat without it sinking, as well as who is able to get the most in their boat.

What we know:
Pwater(1000kg)
Paluminum(2.7 x 10^3)
Mass of the cubes: each cube weighs 20g's.
Dimensions of the cube: 3cm *3 cm * 3cm
Volume of the boat - 24cm *21cm * 4cm.

The P of the block was found by (30%1000)/(3*3*3%100) which comes out to be .074074. (the units need to be kg/m3)

We also know the weight of the block that is being used because W=MG=(20g)(9.8)

Each block added will add an additional force downward, which will counteract Fb (the buoyancy force).

I do not know the mass of the foil, and we are using normal water 1X10^3 for the experiment.

Any help on a formula or ways to achieve it on how to determine the number of cubes that can be added before the boat sinks.

*The foil is 12" x 12" flat, but the shape can be anything to allow for more/less blocks.

 

[Gokul43201]

1. Please be more careful in your description of the problem. We don't know what "P" is supposed to stand for. It is just a symbol and can represent anything! At one point in your post it has units of mass, and at another point it is unitless. This can very easily cause the reader to misinterpret the problem. Unless you are using terms or symbols that are universally used to represent just one thing, always explain what these terms/symbols are.

2. I assume P is actually a density.

3. There are two forces that prevent objects from sinking : (i) a reaction force from surface tension and (ii) buoyancy. I'm going ignore the first one for now (you should look up typical values to estimate this effect and convince yourself about whether or not it may be neglected) and concentrate on the buoyant force.

4. Use a simplified model of the boat to calculate the buoyant force. (see attachment)

5. Write down expressions for the total upward and downward forces on the "boat".

6. Use the fact that the boat is in equilibrium to determine the maximum mass as a function of other variables in the equation.