Saltwater Wood
Buoyancy Questions?
1. 50 cubic centimeters of wood is floating on water, and 50 cubic centimeters of iron is totally submerged. Which has the greater buoyant force on it?
a. the wood
b. the iron
c. both have the same buoyant force
d. cannot be determined without knowing their densities
2. Salt water is more dense than fresh water. A ship floats in both fresh water and salt water. Compared to the fresh water, the volume of water displaced in the salt water is
a. more
b. less
c. the same
d. cannot be determined from the information given
I’m not just looking for the answers. Thank you very much for any explanations!! On the first one, I’m not sure how density pertains to buoyant force, and on the second one, I don’t know how to think about the scenario conceptually. Would the boat displace less salt water because the saltwater is denser and therefore able to hold the ship higher up in the air?
1.
The magnitude of buoyancy force on a floating or submerged object is equal to the weight of the displaced water volume, which is volume of the solid under the water surface. (This fact is known as Archimedes’ principle)
The weight force of displaced liquid is volume times density times acceleration due to earth gravity. Hence:
F_buoyancy = ρ_liquid · V_displaced · g
From the information you can deduce that for the iron object a greater fraction is submerged. Since both objects have the same volume, the volume of of water displaced by the iron object is greater. Therefore it experiences the greater buoyancy force.
b is the correct answer.
In general the density does not pertain buoyancy force directly.
Consider some objects of same volume like in this problem. If the density of the object is smaller than liquid density, it will float. Under this buoyancy force is equal to the weight force of the object. As higher the density and the weight of the object is so greater the displaced volume and the buoyancy force is. But if the the objects density is higher than liquid density the objects is totally submerged, because weight force exceed maximum possible buoyancy force. The displaced volume does not change with density any more. E.g. if you submerge a 50cm³ object of lead it will experience the same buoyancy force as the iron object, although it has a higher density.
Now consider some objects of same mass and you make a different observation.
As long as an object floats, it displaces its own weight. Hence buoyancy is the same for all floating objects of same mass irrespective to their density. But for totally submerged objects it varies, because the volume of an object of fixed mass varies with its density. The lower the density is so greater is it volume and the buoyancy force is.
2.
As pointed out in 1. floating means that buoyancy cancels the effect of gravity acting on the object. That means that buoyancy force and weight force of the object have the same magnitude
F_weight = F_buoyancy
<=>
m_object · g = ρ_liquid · V_displaced · g
=>
V_displaced = m_object / ρ_liquid
That means that the volume displaced by an object decreases for increasing density of the liquid.
Hence the volume displaced in salt water is smaller than in fresh watter.
b is the correct answer.
4000 volts into salt water soaked wood
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