an aluminium cube has a volume of 800cm 3^. If it is total immersed in water, calculate the upthrust acting on it
answer
To calculate the upthrust acting on an aluminum cube immersed in water, we need to consider Archimedes' principle, which states that the buoyant force acting on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
First, we need to determine the weight of the water displaced by the aluminum cube.
1. Determine the mass of the aluminum cube using its volume:
The density of aluminum is approximately 2.7 g/cm^3.
Mass = Volume x Density
Mass = 800 cm^3 x 2.7 g/cm^3
2. Convert the mass from grams to kilograms:
1 kilogram (kg) = 1000 grams (g)
3. Calculate the weight of the water displaced:
Weight = Mass x Gravitational acceleration
Gravitational acceleration is approximately 9.8 m/s^2.
4. Convert the weight from newtons (N) to force:
1 newton (N) = 1 kg x m/s^2
Now we can perform the calculations:
Step 1:
Mass = 800 cm^3 x 2.7 g/cm^3
Step 2:
Mass = (800 x 2.7) / 1000 kg
Step 3:
Weight = Mass x Gravitational acceleration
Weight = (800 x 2.7) / 1000 kg x 9.8 m/s^2
Step 4:
Upthrust = Weight of the water displaced
Upthrust = Weight in newtons (N)
After performing these calculations, we will have the value for the upthrust acting on the aluminum cube when it is immersed in water.
To calculate the upthrust acting on an object immersed in water, you need to use Archimedes' principle. According to this principle, the upthrust or buoyant force acting on an object is equal to the weight of the water displaced by the object.
Here's how you can calculate the upthrust acting on the aluminum cube:
1. Determine the density of water: The density of water is approximately 1 gram per cubic centimeter (g/cm³) or 1000 kilograms per cubic meter (kg/m³).
2. Convert the volume of the aluminum cube to cubic meters: Since the density of water is given in kg/m³, it's best to work with the volume in the same units. So, convert the volume of the cube to cubic meters.
800 cm³ = 800/1000000 m³ = 0.0008 m³
3. Calculate the mass of water displaced: Mass = Density × Volume
Mass of water displaced = 1000 kg/m³ × 0.0008 m³ = 0.8 kg
4. Calculate the upthrust or buoyant force: The upthrust is equal to the weight of the water displaced by the object, which can be calculated using the equation F = m × g, where m is the mass of the water displaced and g is the acceleration due to gravity.
Weight of water displaced = mass of water displaced × gravitational acceleration
Upthrust = 0.8 kg × 9.8 m/s² = 7.84 N
Therefore, the upthrust acting on the aluminum cube when it is completely immersed in water is 7.84 Newtons (N).