buoyancy question

[addis4ever]

Fish control their buoyancy with a gas-filled organ called a swim bladder. The average density of a particular fish's tissues, not including gas in the bladder, is 1080 kg/m^3. If the fish's mass is 8.8 kg, what volume of gas in its swim bladder will keep it in neutral buoyancy-neither sinking nor rising-at a depth where the density of the surrounding seawater is 1028 kg/m^3 ? Neglect the mass of the bladder gas.
I don't know if I did this right but can someone correct me if I'm wrong:

dwater (density of water)
Neutral buoyancy means equilibrium: Fb = Wfish
dwater*Vdisplaced*g = dfish*Vfish*g => Vdisplaced = (dfish/dwater)*Vfish
Vfish = mass/d = 8.8/1080 = 0.00815 m^3
Vdisplaced = (8.8)(0.00815)/1028 = 6.98*10^-5 m^3

Would this be the volume of gas? It seems awfully small to me thats why I'm confused. Any help would be greatly appreciated. Thanx.

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[BerkReviewTeach]

What are the four choices associated with this practice MCAT question? This might be a case where POE works well, given that you get no calculator on the MCAT.

If this were an MCAT question, you could start by saying that the buoyant force must equal mg, which is 88 N (assuming the mass of gas in the bladder is negligible and that g is 10). The volume of seawater that must be displaced to equal 88 N is found using Fbuoyant = V x 1028 x 10.

The volume of the swim bladder can be found by subtracting the volume of fish at a density of 1080 would equal 8.8 kg from the volume of the seawater found above.

If you set it up in a clever way, g could be ignored. Hopefully this gives you a hint at how to do your problem.

 

[Orbo]

The answer is 4.12 * 10^-4 m^3

Up to you to figure out how to reach that answer.

 

[Pisiform]

Since the fish is not going up or down, Fnet is 0. This means that weight of the fish = Buoyant force on the fish.

Weight of the fish is mg (ignore mass of gas) which is also rho(density of fish w/o gas)*g*V(volume of the fish w/o gas)

We know that mass of the fish w/o gas is 8.8kg. So, Density = M/V => 1080 = 8.8/V ... So V = 8.148*10^-3 => Volume of fish w/o gas.

rho(density of fish w/o gas)*g*V(volume of the fish w/o gas) = rho(density of water)*g*V(Volume of fish submerged and since entire fish is submerged this means this is the volume with gas/gills)

1080*10*8.148*10^-3 = 1028*10*V
V = 8.56*10^-3 => volume of the total fish with gas

So, Vol of gas is = 8.56*10^-3 - 8.148*10^-3 = 4.12*10^-4 m^3

 

[Hexon]

Since the fish is not going up or down, Fnet is 0. This means that weight of the fish = Buoyant force on the fish.

Weight of the fish is mg (ignore mass of gas) which is also rho(density of fish w/o gas)*g*V(volume of the fish w/o gas)

We know that mass of the fish w/o gas is 8.8kg. So, Density = M/V => 1080 = 8.8/V ... So V = 8.148*10^-3 => Volume of fish w/o gas.

rho(density of fish w/o gas)*g*V(volume of the fish w/o gas) = rho(density of water)*g*V(Volume of fish submerged and since entire fish is submerged this means this is the volume with gas/gills)

1080*10*8.148*10^-3 = 1028*10*V
V = 8.56*10^-3 => volume of the total fish with gas

So, Vol of gas is = 8.56*10^-3 - 8.148*10^-3 = 4.12*10^-4 m^3

i like your thinking, funny green animal

 

[Pisiform]

i like your thinking, funny green animal

lol my earlier avatar was a goat ..but I lost it and couldnt find it ... its the only animal which is close to that goat