A cube of wood of density 600kg/m^3 is 10 cm long on one side.to what depth will it float in water?
To determine the depth to which the cube will float in water, you need to compare the density of the cube to the density of water. When an object floats in a fluid, it displaces an amount of fluid with weight equal to the weight of the object. In other words, the weight of the fluid displaced by the object is equal to the weight of the object itself.
Here's how to calculate the depth to which the cube will float:
1. Determine the volume of the cube:
The volume of a cube is calculated by multiplying the length of one side cubed.
Given that the length of one side of the cube is 10 cm, the volume will be (10 cm)^3 = 1000 cm^3.
2. Convert the volume to cubic meters:
Since density is usually measured in kg/m^3, convert the volume to cubic meters by dividing by 1,000,000.
1000 cm^3 = 1000/1,000,000 m^3 = 0.001 m^3.
3. Calculate the weight of the cube:
Weight is calculated by multiplying the volume by the density.
Weight = Volume * Density = 0.001 m^3 * 600 kg/m^3 = 0.6 kg.
4. Calculate the weight of the fluid displaced:
Since the cube is fully submerged in water, the weight of the fluid displaced is equal to the weight of the cube.
Weight of fluid displaced = 0.6 kg.
5. Calculate the buoyant force:
The buoyant force is the weight of the fluid displaced, which is equal to the weight of the cube.
Buoyant force = Weight of fluid displaced = 0.6 kg.
6. Determine the density of water:
The density of water at room temperature is approximately 1000 kg/m^3.
7. Calculate the volume of water displaced:
The volume of water displaced is equal to the weight of the fluid displaced divided by the density of water.
Volume = Weight of fluid displaced / Density of water = 0.6 kg / 1000 kg/m^3 = 0.0006 m^3.
8. Calculate the depth of immersion:
The depth of immersion is calculated by dividing the volume of water displaced by the base area of the cube.
Depth = Volume / Base Area = 0.0006 m^3 / (0.1 m * 0.1 m) = 0.006 m = 6 mm.
Therefore, the cube will float to a depth of 6 mm in water.