What is the buoyant force on a 1.200 kg solid steel ball submerged in water? (density of steel is 7,900 kg/m3)

To find the buoyant force, we first need to find the volume of the steel ball. We can use the formula for the volume of a sphere, which is V = 4/3 * π * r^3. But we don't have the radius of the ball. However, we do know the mass (1.200 kg) and the density of steel (7,900 kg/m^3). We can find the volume by rearranging the formula for density (Density = Mass/Volume), to find Volume = Mass/Density.

1. Calculate the volume of the steel ball: Volume = Mass/Density = 1.200 kg / 7,900 kg/m^3 = 0.0001519 m^3

Next, we use 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. In this case, the fluid is water, and the volume of water displaced is equal to the volume of the steel ball. The weight of the water displaced is its mass times the acceleration due to gravity (9.8 m/s^2). The mass of the water displaced is its volume times its density (1,000 kg/m^3).

2. Calculate the mass of the water displaced: Mass = Density * Volume = 1,000 kg/m^3 * 0.0001519 m^3 = 0.1519 kg

3. Calculate the weight of the water displaced: Weight = Mass * gravity = 0.1519 kg * 9.8 m/s^2 = 1.49 N

So, the buoyant force on the steel ball is 1.49 N.