the density of gold is 19.3 x 10^3, what buoyant force does a .60-kg gold crown experience when it is immersed in water?
To calculate the buoyant force experienced by a submerged object, we need to use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
First, let's find the volume of the gold crown. We can use the formula:
Density = Mass / Volume
Rearranging the formula, we get:
Volume = Mass / Density
Given that the mass of the crown is 0.60 kg and the density of gold is 19.3 x 10^3 kg/m^3, we can calculate the volume of the crown:
Volume = 0.60 kg / 19.3 x 10^3 kg/m^3
Volume ≈ 3.11 x 10^-5 m^3
Since the crown is immersed in water, the fluid displaced is water. The density of water is approximately 1000 kg/m^3.
The weight of the fluid displaced (water) is equal to the buoyant force experienced by the crown. We can calculate this using the formula:
Buoyant Force = Weight of Fluid Displaced
Weight of Fluid Displaced = Density of Fluid x Volume x Gravity
Given that the density of water is 1000 kg/m^3, the volume is 3.11 x 10^-5 m^3, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the buoyant force:
Buoyant Force = 1000 kg/m^3 x 3.11 x 10^-5 m^3 x 9.8 m/s^2
Buoyant Force ≈ 0.03 N
Therefore, the buoyant force experienced by the 0.60 kg gold crown when it is immersed in water is approximately 0.03 Newtons.
To find the buoyant force exerted on the gold crown when it is immersed in water, we will use Archimedes' principle. According to the principle, the buoyant force experienced by an object immersed in a fluid is equal to the weight of the displaced fluid.
First, let's find the volume of the gold crown using its mass and density. The density of gold is given as 19.3 x 10^3 kg/m^3.
Density (ρ) = Mass (m) / Volume (V)
Rearranging the formula to solve for volume, we have:
Volume (V) = Mass (m) / Density (ρ)
Substituting the given mass of the gold crown (m = 0.60 kg) and the density of gold (ρ = 19.3 x 10^3 kg/m^3), we can calculate the volume:
V = 0.60 kg / (19.3 x 10^3 kg/m^3)
V ≈ 3.11 x 10^-5 m^3
Now, let's calculate the buoyant force:
Buoyant Force (Fb) = Weight of the Displaced Fluid
The weight of the displaced fluid is equal to the density of the fluid (water) times the volume of the displaced fluid. The density of water is approximately 1000 kg/m^3.
Weight of the Displaced Fluid = Density of Water (ρw) x Volume (V)
Weight of the Displaced Fluid = 1000 kg/m^3 x 3.11 x 10^-5 m^3
Now, we multiply the weight of the displaced fluid by the acceleration due to gravity (g = 9.8 m/s^2) to find the buoyant force:
Buoyant Force (Fb) = Weight of the Displaced Fluid x g
Buoyant Force (Fb) = (1000 kg/m^3 x 3.11 x 10^-5 m^3) x 9.8 m/s^2
Calculating this expression will give you the buoyant force experienced by the gold crown when it is immersed in water.