Neutral Buoyancy of a fish

In summary, to be neutrally buoyant a fish's body must be filled with air at a density of 1.28 kg/m3.
  • #1
Physicsdude13
6
0

Homework Statement



The average density of the body of a fish is 1147.0 kg/m3. To keep from sinking, fish have an air bladder filled with air. If the density of air is 1.28 kg/m3, what percentage of a fish's body must be filled with air to be neutrally buoyant? (Note: Enter your percentage without a unit attached.)

Homework Equations



/rho avg = Total mass of object / Total volume of object
/rho avg = 1000 kg/m^3

The Attempt at a Solution



/rho avg = Mo / Vo (Total mass/ divided by total volume)

Mo = Ma + Mf (Ma= mass of air and Mf= mass of fish)

Ma= 1.28Va (density of air x volume of air)

Mf = 1147Vf (density of fish x volume of fish)

Now subsituting all the equations together I get...

/rho avg = 1000 = (1.28Va + 1147 (Vo-Va)) / Vo

and isolating for Va/ Vo = .128 x100% = 12.8 %

I also did this to get get Ma / Mo = 0.016% ... but neither answer is right :S. Can anyone tell me what I did wrong, or whether their answer is wrong? Its much appreciated thanks!
 
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  • #2
I get pretty close to you, about 13%.

I think your (Vo-Va) is wrong and seems to be assuming the tissues of the fish are compressed. Not so, the tissues are incompressible and the fish actually has to get bigger!

What is the right answer supposed to be?
 
  • #3
Well with the (Vo - Va) thing... i forgot to show my steps with that. Basically orginially its 1147 times the volume of the fish... and I assumed that volume of fish plus volume of air is equal to volume of object. Thus Vo = Va + Vf and I isolated for Vf and subsituted it into the equation.

As for the answer I am unsure, it is an online quiz thing... have 10 attempts to get the answer. So far I tried like those few ways.
 
  • #4
The answer was 14.7%. Apparently it wanted the volume of the air to the volume of the fish, not relative to the total volume. Therefore instead of substituting to get rid of Vf I'd need to substitute to get rid of Vo and Isolate for Va/ Vf.

Thanks for the help though!
 

What is neutral buoyancy of a fish?

Neutral buoyancy of a fish refers to the state in which the fish is able to remain suspended at a specific depth in the water without sinking or floating. This is achieved when the fish's overall density is equal to the density of the surrounding water.

How do fish maintain neutral buoyancy?

Fish maintain neutral buoyancy through a combination of physiological and behavioral adaptations. These include their swim bladder, which allows them to control their overall density, and their movements and positioning in the water.

Why is neutral buoyancy important for fish?

Neutral buoyancy is important for fish as it allows them to conserve energy while swimming, as they do not have to constantly adjust their position in the water. It also enables them to move more efficiently and accurately, making it easier for them to catch prey and avoid predators.

Can fish control their buoyancy?

Yes, fish have the ability to control their buoyancy through their swim bladder. This organ is filled with gas, which the fish can adjust to change their overall density and achieve neutral buoyancy.

Does the depth of the water affect a fish's neutral buoyancy?

Yes, the depth of the water can affect a fish's neutral buoyancy. As the pressure increases with depth, the density of the water also increases, making it more difficult for the fish to maintain neutral buoyancy. To adjust, fish may change the amount of gas in their swim bladder or adjust their movements and positioning in the water.

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