Question

Explain the relationship Fb = PVg

Answer 1

In simple terms, buoyancy is the ability of an object to float.
Whether or not a given object will float is determined by the buoyant force on the object.
This force is caused by the difference between the pressure at the top of the object, which pushes it downward and the pressure at the bottom of the object which pushes it upward. Because the pressure at the bottom of the object is always greater than the pressure at the top, every submerged object feels an upward buoyant force.
The magnitude of this buoyant force is equal to the weight of the fluid that is displaced by the submerged object.

Step 1:
Formula for Buoyant Mass m(b) m(b) = m(object) x (1- (p(fluid)/ p(object))) m(object)= true mass of the object p(object)= average density of the object p(fluid)= average density of the surrounding fluid If the fluid density is greater than the average density of the object, the object floats. If less, the object sinks.

Step 2:
Formula for Buoyant Force: F(buoyant) = -pVg p = density of the fluid V = volume of the object being submerged g = standard gravity on Earth (~ 9.81 N/kg)

Step 3:
Archimedes Principle: "When a solid body is partially or completely immersed in water, the apparent loss in weight will be equal to the weight of the displaced liquid." Formula for Density of immersed object relative to the density of the fluid object is immersed in: Relative Density = Weight / (Weight - Apparent Immersed Weight)