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Will someone please help me understand the relationship between buoyancy and specific gravity? I'm having a hard time with this for some reason.
Thanks!
Thanks!
Relationship between buoyancy force and specific gravity
- Thread starter bretonnia
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No worries, I hated this concept when I was studying physics!
Your question is vague, so I'll just walk you through my understanding and see if it helps. There are two possible scenarios here: one where an object is floating, and one where the object is submerged.
Keep in mind the definition of the buoyant force F(b), which is equal to the weight of the surrounding liquid displaced by the object.
Now, if the object is floating, we know that the buoyant force MUST also be equal to the full weight of the OBJECT, since the object is in static equilibrium (no acceleration, no net force). This means that F(b) = R(l)*V(s)*g, where R(l) is the density of the surrounding liquid and V(s) is the volume submerged. At the same time, we know that weight = mg, but we can rewrite this as weight = R(o)*V(o)*g, where R(o) is density of the object and V(o) is the volume of the object, since mass = density * volume. Since Fb = weight, we can set R(l)*V(s)*g = R(o)*V(o)*g and rearrange to get V(s)/V(o) = R(o)/R(l). Notice that if the surrounding liquid is water, R(o)/R(l) is the definition of the specific gravity of R(o). Thus, V(s)/V(o) = specific gravity of R(o) if it's floating in water. The qualitative way to interpret this is that the % volume of the object that is submerged is equal to the ratio of the density of the object to the surrounding fluid. This should make sense; when the densities are equal, notice V(s)/V(o) becomes 1, and the object is fully submerged.
For the second case, if the object is completely submerged already (sitting at the bottom of the pool, for example) , then clearly the buoyant force wasn't sufficient to balance the weight of the full object. But we do know that F(b) = R(l)*V(o)*g, since the object's volume is now fully submerged. The weight of the object can again be written as weight = R(o)*V(o)*g. Now, if we divide weight by Fb, we get weight/F(b) = R(o)/R(l), since V(o) and g cancel out. Notice again what this means: the ratio of the weight of a completely submerged object to the buoyant force acting on it is equal to the ratio of the density of the object to the density of the liquid. If the liquid happens to be water, then R(o)/R(I) is the specific gravity of the object.
As a final note, notice for both bolded expressions that if the liquid is not water, you could also dividie both the top and bottom of the expression by R(w) (density of water) and rewrite the same expression of R(o)/R(I) as [R(o)/R(w)]/[R(l)/R(w)]. But R(o)/R(w) is the definition of the specific gravity of the object, and R(l)/R(w) is the definition of the specific gravity of the water. Thus, in the bolded expression wherever we wrote R(o)/R(l), we could equivalently write S(o)/S(l) if the liquid isn't water, and thus relate the weight and buoyant forces in each scenario to the specific gravities of the object and liquid.
Sorry for the wall of text. Hope that helps, let me know if still confused.
Your question is vague, so I'll just walk you through my understanding and see if it helps. There are two possible scenarios here: one where an object is floating, and one where the object is submerged.
Keep in mind the definition of the buoyant force F(b), which is equal to the weight of the surrounding liquid displaced by the object.
Now, if the object is floating, we know that the buoyant force MUST also be equal to the full weight of the OBJECT, since the object is in static equilibrium (no acceleration, no net force). This means that F(b) = R(l)*V(s)*g, where R(l) is the density of the surrounding liquid and V(s) is the volume submerged. At the same time, we know that weight = mg, but we can rewrite this as weight = R(o)*V(o)*g, where R(o) is density of the object and V(o) is the volume of the object, since mass = density * volume. Since Fb = weight, we can set R(l)*V(s)*g = R(o)*V(o)*g and rearrange to get V(s)/V(o) = R(o)/R(l). Notice that if the surrounding liquid is water, R(o)/R(l) is the definition of the specific gravity of R(o). Thus, V(s)/V(o) = specific gravity of R(o) if it's floating in water. The qualitative way to interpret this is that the % volume of the object that is submerged is equal to the ratio of the density of the object to the surrounding fluid. This should make sense; when the densities are equal, notice V(s)/V(o) becomes 1, and the object is fully submerged.
For the second case, if the object is completely submerged already (sitting at the bottom of the pool, for example) , then clearly the buoyant force wasn't sufficient to balance the weight of the full object. But we do know that F(b) = R(l)*V(o)*g, since the object's volume is now fully submerged. The weight of the object can again be written as weight = R(o)*V(o)*g. Now, if we divide weight by Fb, we get weight/F(b) = R(o)/R(l), since V(o) and g cancel out. Notice again what this means: the ratio of the weight of a completely submerged object to the buoyant force acting on it is equal to the ratio of the density of the object to the density of the liquid. If the liquid happens to be water, then R(o)/R(I) is the specific gravity of the object.
As a final note, notice for both bolded expressions that if the liquid is not water, you could also dividie both the top and bottom of the expression by R(w) (density of water) and rewrite the same expression of R(o)/R(I) as [R(o)/R(w)]/[R(l)/R(w)]. But R(o)/R(w) is the definition of the specific gravity of the object, and R(l)/R(w) is the definition of the specific gravity of the water. Thus, in the bolded expression wherever we wrote R(o)/R(l), we could equivalently write S(o)/S(l) if the liquid isn't water, and thus relate the weight and buoyant forces in each scenario to the specific gravities of the object and liquid.
Sorry for the wall of text. Hope that helps, let me know if still confused.
