Question

consider a 3.1 kg freshwater fish whose tissues have an average density of 1050 kg/m3 . to what volume in ml must the swim bladder be inflated for the fish to be neutrally buoyant at the surface?

Answer 1

To achieve neutral buoyancy at the surface, a 3.1 kg freshwater fish with a tissue density of 1050 kg/m³ must inflate its swim bladder to a volume of 3100 mL.

Step-by-step explanation:

To determine the volume to which a freshwater fish's swim bladder must be inflated to make it neutrally buoyant at the surface, we apply the principle of buoyancy. The fish must displace a volume of water equal to its mass to float neutrally. Given the mass of the fish is 3.1 kg and the density of freshwater is approximately 1000 kg/m³, the volume of water displaced must be equivalent to the mass of the fish divided by the density of freshwater:

V = m / ρ
= 3.1 kg / 1000 kg/m³
= 0.0031 m3

Converting this to milliliters (1 m3 = 106 mL), we get:

V = 0.0031 m³ × 106 mL/m³
= 3100 mL

Therefore, the fish's swim bladder must be inflated to a volume of 3100 mL to achieve neutral buoyancy at the water's surface.

Answer 2

To achieve neutral buoyancy, the volume that the swim bladder must be inflated can be calculated by equating the weight of the fish to the weight of the water it needs to displace.

Step-by-step explanation:

To determine the volume that the swim bladder of a 3.1 kg freshwater fish must be inflated to achieve neutral buoyancy, we start with the principle of buoyancy which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The fish is neutrally buoyant when the gravitational force downward is equal to the buoyant force pushing upwards.

The weight of the fish in Newtons is calculated by multiplying its mass by the acceleration due to gravity: Weight of fish = 3.1 kg × 9.81 m/s².

The weight of water displaced, which equals the buoyant force when the fish is neutrally buoyant, must match this weight. Since the fish's tissues have an average density (1050 kg/m³) greater than freshwater (1000 kg/m³), the fish needs to displace additional water volume with a swim bladder.

To find this additional volume, we equalize the fish's weight with the buoyant force using the equation: Weight of fish = Density of water × Volume displaced × 9.81 m/s². After finding the volume in cubic meters, we then convert that to milliliters (1 m³ = 1,000,000 ml).