An iceberg (specific gravity 0.917) floats in the ocean (specific

Cynthia Bell

Cynthia Bell

Answered question

2021-12-16

An iceberg (specific gravity 0.917) floats in the ocean (specific gravity 1.025 ). What percent of the volume of the iceberg is under water?

Answer & Explanation

Gerald Lopez

Gerald Lopez

Beginner2021-12-17Added 29 answers

Start by calculating the force of weight of the iceberg:
Fw=SGiceγH2OV
=0.917γH2OV
=0.91762.4lbft3V
=57.22 V lb
The buoyancy force that acts upwards and opposes the force of weight is:
Fb=SGsea waterγH2OV
Where V' is the volume of the submerged part of the iceberg. Substituting the known values we obtain:
Fb=1.02562.4lbft3V
=63.96 V lb
We have two unknowns here, C and V', but since the question is to find the percent submerged volume, we can relate the formula for the percentage to the obtained expressions for forces, and solve for percentage:
Fb=Fw
57.22 V lb=63.96 V lb
VV=57.2263.96
=0.895
Since the ratio is 0.895, the percentage of submerged volume (versus the total volume) is:
V(%)=89.5%
aquariump9

aquariump9

Beginner2021-12-18Added 40 answers

For this question starting by calculating the force of weight. But the iceberg, we can right after blue, that will be equals two specific gravity of eyes multiplied by gamma quarter, multiplied by volume. Week. Okay, so substituting the values, we get 0.917 Multiplied by £62.4.4 feet. Q. Molecular by feet. So from here we get F W equals two 57 point double too. We lb. Okay, so now buoyancy force that acts up our and opposes the force of weight is equal to F B equals two S. G.
Specific gravity of seawater Multiplied by gamma water, multiplied by redish. Okay, so substituting the values specific gravity of seawater is 1.025. multiplied by 62.4, manipulated by readers. So from here after solving we get FB equals two 63.96. Videsh held power. Now we have to announce V and whitish since the question is to find the percentage of so much volume. So uh we can relate the formula And we can write at the equals two FW.
So substituting both the values, we get 63.96 videsh that is equals to 57 point double two with. Okay, so from here we get videsh by V. That is equals to 57 point double too. They went by 63.96. And after solving, we get 0.895. Okay, so the ratio is 0.895. So the percentage of so much volume that will be equal to percentage. We dash Is equals to 89.5%. So this is the answer for that question. Okay, this is a lot to answer for that question.
Don Sumner

Don Sumner

Skilled2023-05-29Added 184 answers

Result:
89.5%
Solution:
Let's denote the density of water as ρw, the density of the iceberg as ρi, and the volume of the iceberg as Vi.
The weight of the water displaced by the submerged portion of the iceberg is equal to the weight of the iceberg itself. Therefore, we can set up the following equation:
ρw·Vw=ρi·Vi
We know that specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). So we can write:
ρw={specific gravity of water}×{density of water}
ρi={specific gravity of iceberg}×{density of water}
Substituting these values into the equation, we have:
{specific gravity of water}×{density of water}·Vw={specific gravity of iceberg}×{density of water}·Vi
The density of water cancels out, giving us:
{specific gravity of water}·Vw={specific gravity of iceberg}·Vi
Now, let's denote the volume of the submerged portion of the iceberg as Vs. The volume of the iceberg above the waterline is then given by Va=ViVs.
We can rewrite the equation as:
{specific gravity of water}·(Vw+Vs)={specific gravity of iceberg}·Vi
Solving for Vs, we get:
Vs=(specific gravity of icebergspecific gravity of water1)·Vi
To find the percentage of the volume of the iceberg that is underwater, we divide Vs by Vi and multiply by 100:
{Percentage underwater}=VsVi×100
Substituting the value of Vs from the previous equation:
{Percentage underwater}=((specific gravity of icebergspecific gravity of water1)·ViVi)×100
Simplifying further:
{Percentage underwater}=(specific gravity of icebergspecific gravity of water1)×100
Given that the specific gravity of the iceberg is 0.917 and the specific gravity of water is 1.025, we can substitute these values into the equation:
{Percentage underwater}=(0.9171.0251)×100
Calculating this expression gives us:
{Percentage underwater}=0.895×100=89.5%
Therefore, approximately 89.5% of the volume of the iceberg is underwater.
nick1337

nick1337

Expert2023-05-29Added 777 answers

To solve this problem, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Let's denote the density of water as ρw and the density of the iceberg as ρi. The specific gravity is defined as the ratio of the density of a substance to the density of water. Therefore, we have:
ρw={density of water}=1{g/cm}3
ρi={density of iceberg}=0.917×ρw=0.917{g/cm}3
Now, let's assume that the volume of the iceberg is Vi and the volume of the submerged part is Vs. We can express the volume of the water displaced as Vw=ViVs.
Since the specific gravity of the iceberg is less than that of water, we know that the iceberg will float. This means that the buoyant force acting on the iceberg is equal to its weight. The weight of the iceberg is given by:
Wi=ρi×g×Vi
where g is the acceleration due to gravity.
The buoyant force acting on the iceberg is given by:
Fb=ρw×g×Vw
Since the buoyant force is equal to the weight of the iceberg, we have:
ρw×g×Vw=ρi×g×Vi
Now, let's solve for Vs, which represents the submerged volume:
Vs=ViVw
Substituting the expression for Vw in terms of Vi and Vs, we have:
Vs=Vi(ViVs)
Vs=2VsVi
Vs=12Vi
Finally, to find the percentage of the volume of the iceberg that is underwater, we divide Vs by Vi and multiply by 100:
{Percentage of volume underwater}=VsVi×100=12ViVi×100=12×100=50%
Therefore, 50% of the volume of the iceberg is underwater.
RizerMix

RizerMix

Expert2023-05-29Added 656 answers

Let's denote the volume of the iceberg as Vi and the volume of water displaced by the iceberg as Vw. According to Archimedes' principle, the buoyant force acting on the iceberg is equal to the weight of the water displaced:
Fb=Fg
Vw·ρw·g=Vi·ρi·g
where ρw is the density of water, ρi is the density of the iceberg, and g is the acceleration due to gravity.
We are given that the specific gravity of the iceberg, SGi, is 0.917, which is the ratio of its density to the density of water:
SGi=ρiρw
Rearranging this equation, we can express the density of the iceberg in terms of the specific gravity:
ρi=SGi·ρw
Substituting this expression into the equation above, we can rewrite the equation as:
Vw·ρw·g=Vi·SGi·ρw·g
Canceling out the common factors of ρw and g:
Vw=Vi·SGi
Now, we can calculate the percentage of the volume of the iceberg that is underwater:
Percentage=VwVi·100
Substituting the value of Vw from the previous equation:
Percentage=Vi·SGiVi·100
Simplifying:
Percentage=SGi·100
Now, let's substitute the given values: SGi=0.917.
Percentage=0.917·100
Calculating:
Percentage=91.7
Therefore, approximately 91.7% of the volume of the iceberg is underwater.

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