A piece of wood of mass 60kg and density 600kg/m3 flows in water of density of 1000kg/m3.calculate (a) volume of water that the wood displaced (b) the fraction of volume of mass and water
short answer:
40% above water
60% below water :)
long answer:
volume of wood = 60 kg (1 m^3/600kg)
= 0.1 m^3
volume of wood under water (see Archimedes)
= 60 kg (1 m^3/1000kg)
= 0.06 m^3
To calculate the volume of water that the wood displaced, we can use the formula for displacement:
(a) Volume of water displaced = Volume of wood
Since we know the density of the wood (600 kg/m^3) and the mass of the wood (60 kg), we can use the formula for density to find the volume of the wood:
Density = Mass / Volume
Volume = Mass / Density
Volume of wood = 60 kg / 600 kg/m^3 = 0.1 m^3
Therefore, the volume of water displaced by the wood is also 0.1 m^3.
(b) To calculate the fraction of volume of the mass and water, we need to compare the volume of the wood to the total volume of the wood and water combined.
The total volume of the wood and water can be calculated using the formula:
Total Volume = Volume of Wood + Volume of Water
Since the water displaced has the same volume as the wood, the total volume is:
Total Volume = 0.1 m^3 + 0.1 m^3 = 0.2 m^3
Now, to calculate the fraction of volume of the mass and water, we divide the volume of the wood by the total volume:
Fraction of Volume = Volume of Wood / Total Volume
Fraction of Volume = 0.1 m^3 / 0.2 m^3 = 0.5
Therefore, the fraction of the volume of the wood and water is 0.5.
To solve this problem, we'll make use of Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Here's how you can find the answers to the given questions:
(a) The volume of water that the wood displaces:
To find the volume of water displaced by the wood, you can make use of the formula:
volume = mass / density
Given that the mass of the wood is 60 kg and its density is 600 kg/m^3, we can substitute these values into the formula:
volume = 60 kg / 600 kg/m^3
By simplifying, you get:
volume = 0.1 m^3
Therefore, the wood displaces 0.1 cubic meters of water.
(b) The fraction of volume of mass and water:
To find the fraction of the wood's volume to the volume of water displaced, you can use the following formula:
fraction = volume of wood / volume of water
Given that the volume of wood is the same as its mass (since the density is given), the fraction can be calculated as:
fraction = 0.1 m^3 / 0.1 m^3
By simplifying, you get:
fraction = 1
Therefore, the fraction of the wood's volume to the volume of water displaced is 1 or 100%.