What is the Buoyancy force exerted on a 180kg iron anchor when it is immersed in seawater? The density of iron is 7.8×103 kg/m3 and that of seawater is 1.03 × 103 kg/m3 .
To calculate the buoyancy force exerted on the iron anchor when it is immersed in seawater, we need to understand the concept of buoyancy and Archimedes' principle.
Buoyancy is the upward force exerted by a fluid on an object immersed in it. It depends on the density of the fluid and the volume of the displaced fluid. Archimedes' principle states that an object immersed in a fluid experiences a buoyant force equal to the weight of the fluid displaced by the object.
To calculate the buoyancy force, we need to find the volume of the iron anchor and determine the volume of seawater it displaces.
First, let's find the volume of the iron anchor using its density and mass:
Density of iron (ρ_iron) = 7.8 × 10^3 kg/m^3
Mass of iron anchor (m) = 180 kg
We can use the formula for density (ρ = m/V) to derive the formula for volume (V = m/ρ):
Volume of iron anchor (V_iron) = m/ ρ_iron = 180 kg / 7.8 × 10^3 kg/m^3
Next, let's determine the volume of seawater displaced by the iron anchor. Since the anchor is fully immersed in seawater, the volume of water displaced will be equal to the volume of the iron anchor.
Volume of seawater displaced (V_water) = Volume of iron anchor (V_iron)
Now, we can calculate the buoyancy force using the formula:
Buoyancy force (F_buoyancy) = Volume of seawater displaced (V_water) × Density of seawater (ρ_water) × Gravitational acceleration (g)
Density of seawater (ρ_water) = 1.03 × 10^3 kg/m^3
Gravitational acceleration (g) = 9.8 m/s^2
Substituting the values, we have:
Buoyancy force (F_buoyancy) = (V_iron) × (ρ_water) × (g)
By substituting the volume of the iron anchor and the values for seawater density and gravitational acceleration, you can calculate the buoyancy force exerted on the iron anchor when it is immersed in seawater.