A cubical block of wood of side 0.5 m floats in water. Given that the densities of wood and water are 800 and 1000 kg/m3 respectively
Calculate the depth of the block immersed in water.
Depth = Dwo/Dwa * h = (800/1000) * 0.5 = 0.40 m.
a cube of sides 0.5 m floats in a large tank of water at a height of 0.3 m above the surface ..calculate
1. weight of the cube
2. vertical upthrust given to the cube by the water
3. volume of water displaced by the cube
To calculate the depth of the block immersed in water, we need to use the principle of buoyancy. This principle states that for an object to float in a fluid, the upward buoyant force must equal the weight of the object.
To calculate the buoyant force, we can use Archimedes' principle, which states that the buoyant force acting on a submerged or floating object is equal to the weight of the fluid displaced by the object.
First, let's find the weight of the block of wood. The weight of an object can be calculated using the formula:
Weight = Mass x Gravity
Given that the density of wood is 800 kg/m³ and the side length of the block is 0.5 m, we can calculate the mass of the block using the formula:
Mass = Density x Volume
Since the block is a cube, the volume can be calculated by raising the side length to the power of 3:
Volume = Side Length³
Now, let's calculate the weight of the block of wood:
Mass = Density of wood x Volume
Mass = 800 kg/m³ x (0.5 m)³
Next, we calculate the volume of water displaced by the block when it is immersed. Since the block is a cube and we want to find the depth, which corresponds to the height of the block submerged, the volume of water displaced is equal to the cross-sectional area of the block multiplied by the depth:
Volume of water displaced = Cross-sectional Area x Depth
The cross-sectional area of the block is the area of one of its faces:
Cross-sectional Area = Side Length²
Finally, we can now calculate the depth of the block immersed in water using the equation:
Buoyant force = Weight of the block
Buoyant force = Density of water x Volume of water displaced x Gravity
Density of water x Cross-sectional Area x Depth x Gravity = Mass x Gravity
Now, we can solve for the depth of the block immersed in water:
Depth = (Mass x Density of water) / (Density of wood x Side Length²)