a solid cube of side l floats on water with 20% of its volume under water. Cubes identical to it are piled one by one on it. Assumes that the cubes do not slip or topple and contact between their surfaces is perfect. How many cubes are required to submerge one cube completly?
Five, counting the submerged cube. The cubes have 1/5 the density of water. Five of them have a weight of 5*0.2*M*g, where M is the mass of one cube, IF it were water. That weight is balanced by the buoyancy force of a single cube, M*g.
To determine how many cubes are required to completely submerge one cube, we need to understand the relationship between the volume of the cube and the volume of water it displaces.
1. Let's start by determining the volume of the cube underwater. We are given that 20% of its volume is submerged. This means that 80% of its volume is above the water. Since the cube is solid, all its sides are submerged to the same extent.
2. Next, we need to understand the relationship between the volume of the cube underwater and the volume of water it displaces. According to Archimedes' principle, the volume of water displaced by an object submerged in a fluid is equal to the volume of the object itself.
3. Since the cube is completely submerged when additional cubes are piled on it, we can rely on the same principle for each extra cube added. Each new cube completely displaces the volume of water equal to its own volume.
4. To find the number of cubes required to fully submerge the first cube, we need to determine how many times the volume of the initial cube equals the volume of the submerged part of the cube.
Let's say the side length of the cube is 'a'. The volume of the cube is given by V = a^3.
Since 80% of this cube is above the water, the submerged volume is 0.8 * V = 0.8 * a^3.
Now, let's determine the volume of each individual cube we are adding. Since these cubes are identical to the original cube, they have the same side length 'a'.
Therefore, each cube has a volume of a^3.
To determine the number of cubes required, we divide the submerged volume of the first cube by the volume of each additional cube:
0.8 * a^3 / a^3 = 0.8 cubes
Since we cannot have a fraction of a cube, and we need at least one full additional cube to submerge the first cube completely, we can conclude that two cubes are required to submerge one cube completely.
Therefore, the answer to the question is: 2 cubes are needed to submerge one cube completely.