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.

 

[sir-pinski]

Buoyancy and density are two important concepts in fluid mechanics that play a crucial role in determining the stability and floating ability of objects in a liquid. Buoyancy is the upward force exerted by a fluid on an object immersed in it, while density is the measure of how tightly packed the particles in a substance are. In your experiment, the goal was to determine the maximum number of cubes that can be added to your aluminum foil boat before it sinks. To do this, we need to consider the buoyancy and density of the materials involved.

First, let's look at the density of the water and aluminum. Water has a density of 1000 kg/m3, while aluminum has a density of 2.7 x 103 kg/m3. This means that aluminum is much denser than water, so it will sink in water unless it is shaped in a way that allows it to displace enough water to equal its weight.

Next, we need to consider the density of the cubes. Each cube has a mass of 20 grams and dimensions of 3cm x 3cm x 3cm. Using the formula for density, we can calculate that the density of each cube is 0.074074 kg/m3. This is much less than the density of water, so the cubes will float in water.

Now, let's think about the buoyancy force. As you correctly mentioned, the buoyancy force is equal to the weight of the water displaced by the object. In this case, the water displaced by the boat will be the same as the water displaced by the cubes. So, for each cube added to the boat, there will be an additional force pushing upwards, counteracting the weight of the boat and any previously added cubes. This means that the boat can hold more cubes as long as the buoyancy force is greater than the weight of the boat.

To determine the maximum number of cubes the boat can hold, we need to consider the volume of the boat. You mentioned that the boat has dimensions of 24cm x 21cm x 4cm, which gives a total volume of 2016 cm3. To convert this to m3, we divide by 106, giving a volume of 0.002016 m3. This is the volume of water that needs to be displaced by the boat to keep it afloat.

Now, we can use the density of the cubes and the volume of the boat to calculate the