a wooden board 10cm. thick floats in water (1000kg/m3) with its upper surface parallel to and 3cm above the water surface.what is the density of the wood?
To determine the density of the wooden board, we can make use of Archimedes' principle, which states that an object that is submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
In this case, the wooden board is floating partially submerged in water, with its upper surface 3cm above the water surface. This means that the lower part of the board is submerged in the water, displacing an amount of water equal to the volume of the submerged portion.
Let's calculate the volume of the submerged portion first:
The thickness of the wooden board is given as 10cm, and the 3cm portion is submerged, leaving 7cm above the water surface. Since the upper surface of the board is parallel to the water surface, we can assume that the submerged portion has the same area as the upper surface.
Therefore, the volume of the submerged portion is:
Volume = Area × Thickness
Volume = (Area of upper surface) × 3 cm
Now, let's calculate the density of the board:
Since the board is floating in water, the buoyant force is equal to the weight of the water displaced by the submerged portion. The buoyant force can be calculated using the formula:
Buoyant Force = (Density of fluid) × (Volume of submerged portion) × (Acceleration due to gravity)
The buoyant force must be equal to the weight of the board in order for it to float. Thus, we can equate the buoyant force to the weight of the wooden board:
(Buoyant Force) = (Weight of wooden board)
(Density of fluid) × (Volume of submerged portion) × (Acceleration due to gravity) = (Weight of wooden board)
Now, solving for the density of the wooden board:
(Density of wooden board) = (Weight of wooden board) / (Volume of submerged portion)
To get the weight of the board, we need to know its mass. Assuming the board is made of solid wood with uniform density, we can calculate its weight using the formula:
Weight = (Mass of wooden board) × (Acceleration due to gravity)
However, without knowing the mass of the wooden board, we cannot calculate its weight or density accurately.