Below is my personal discussion about the formula:
Buoyant Force: Fb = ρ(fluid)Vg
Note: This is one of the formulas we learn for the topic of Fluids
Can you go over my statements below and tell me if they are correct?
Buoyant Force: Fb = ρ(fluid)Vg:
(1) When an object is submerged or its whole body volume is placed into a fluid, the amount of fluid that sort of falls out of the system is equal to the volume of the object. Since the buoyant force is always equal to the weight of the fluid that has been kicked out, so to speak, then Fb = ρ(fluid)Vg, where V is the volume of fluid that has been kicked out, or V is also equal to the whole body volume of the object, since the whole body volume of the object is equal to the volume of fluid that has been kicked out.
The weight of the object then, is Weight = mg, which is also Weight = ρ(object)Vg, since mass = ρV.
(2) There are then two forces in action when considering totally submerged objects: Fb, which is always equal to the weight of the volume of fluid that has been kicked out due to the object's volume, and weight, which is the weight of the totally submerged object. Since the volumes of both equations (Fb = ρ(fluid)Vg and Weight = ρ(object)Vg) are equal as indicated above, and the gravitational acceleration is a constant, then the only other thing that matters is the density of the object compared to that of the fluid. If the density of the object is greater, than the object's weight force will be greater, causing the object to sink down within the fluid.
3) Likewise, for an object that has been totally submerged, if the density of the object is less than that of the fluid, then the buoyant force exceeds the Weight, causing the object to rise upwards within the fluid, until the two forces equal each other.
And right here, I don't understand what is actually going on: In order for the forces to cancel each other, the object has to rise up. Let's say it rises all the way up to the surface of the fluid such that the object floats, where half of the object's volume is out of the fluid and half of its volume is still submerged in the fluid. Since it is floating, it is not rising or sinking within the fluid, so Fb and Weight must be equal. Fb = ρ(fluid)Vg and Weight = ρ(object)Vg. We can ignore "g" since it's a constant. Then it becomes: Fb = ρ(fluid)V and Weight = ρ(object)V. How does ρ(fluid)V = ρ(object)V?
What I think is (I may be wrong), since the object still has half of its volume totally submerged in the fluid, then considering this submerged half as a body by itself, such a body will sort of kick out a volume of fluid equal to its own volume (volume of half of the entire object). Therefore, the volumes of the equations, ρ(fluid)V = ?(object)V, are equal, so we can ignore that. Then we get: ρ(fluid) = ρ(object).
That is rather confusing: How can the density of the object eventually be equal to that of the fluid just because some portion of the object is submerged, while the remainder of the object is outside of the fluid? Is it because the volume of the object submerged in the water is smaller when it floats, so since ρ = m/V and volume is smaller, then density increases, and such a density is increased all the way up to equal the density of the fluid? But if this is so, don't we also have to account for the mass that is no longer submerged in the fluid (or the mass that is sticking out of the fluid)? If the volume submerged is smaller, then so is the mass. Do the ratios of the mass and volume work out just right so that the density of the object equals the density of the fluid?
Then there is this formula:
Fraction of object that is submerged = density of floating object / density of fluid
Can you explain this formula relating to what I stated in statement 3?
Floating and buoyancy.
An object will float if its density is less than that of the fluid in which it is floating. (Lets ignore the case when they are exactly equal for simplicity).
Archimedes - there is an upthrust which is equal to the WEIGHT of the fluid displaced (i.e. volume of displaced fluid x density of displaced fluid x acceleration of Earth's gravity).
The formula you quoted:
Buoyant force = density of fluid x volume of fluid displaced x g is correct as long as you realise that this is just what I call the upthrust - remember that there is also the weight of the object acting downwards and it is because these two forces balance that the object floats.
No if the density of the object is less than that of the fluid it will need a smaller volume of fluid than its own volume to provide the upthrust to balance its weight - hence it floats with some of its volume outside the water.
So:
The density of the fluid x volume of fluid displaced x g = density of solid x volume of solid immersed x g
And this gives:
Density of fluid x volume of fluid displaced= density of solid x volume of solid