BIO Fish Navigation. (a) As you can tell by watching them in an aquarium, fish are able to remain at any depth in water with no effort. What does this ability tell you about their density? (b) Fish are able to inflate themselves using a sac (called the swim bladder) located under their spinal column. These sacs can be filled with an oxygen–nitrogen mixture that comes from the blood. If a 2.75-kg fish in freshwater inflates itself and increases its volume by 10%, find the net force that the water exerts on it. (c) What is the net external force on it? Does the fish go up or down when it inflates itself?
Solution to 52P Step 1 of 3 (a) The fish neither floats on water nor it sinks. It can wade through the water. Thus the average density of fish should be equal to that of water to remain at any depth inside water. If the density of fish is large compared to that of water, it will sink. On the other hand if the density is less compared to that of water, it floats. The fish regulates its density through the swim bladder which is filled with air. (b) We have to find the net force exerted on the fish by the water. Mass of the fish=2.75kg Initial volume =V Final volume =1.1V………………………………….(V’=V+V) When the fish is fully submerged in water, the buoyant force should be equal to the weight of the water displaced by the fish. Step 2 of 3 Buoyant force exerted on fish= Weight of the water displaced by fish=2.75kg X9.8=27N According to Archimedes principle, Weight of the water displaced=Buoyant force exerted on fish Buoyant force on fish=F =BN