Question

Some fish have a density slightly less than that of water and must exert an extra force to stay submerged through swimming. what force must a grouper (85.0kg) exert to stay submerged in salt water (1025 kg/m3) if its body density is 1015 kg/m3?

Answer 1

The force that a grouper must exert to stay submerged in salt water can be calculated using Archimedes' principle. According to this principle, the weight of the water displaced by the fish must be equal to the buoyant force acting on it. The force can be determined by multiplying the volume of the fish by the density of salt water and the acceleration due to gravity.

Step-by-step explanation:

The force that a grouper must exert to stay submerged in salt water can be calculated using Archimedes' principle. According to this principle, the weight of the water displaced by the fish must be equal to the buoyant force acting on it.

The weight of the water displaced can be calculated by multiplying the volume of the fish by the density of salt water. The buoyant force can be calculated by multiplying the density of salt water by the acceleration due to gravity and the volume of the fish.

Using the given information, we can calculate the volume of the fish by dividing its mass by its body density. The weight of the water displaced is equal to the volume of the fish multiplied by the density of salt water. Finally, the force that the grouper must exert to stay submerged is equal to the weight of the water displaced.

Let's calculate:

1. Calculate the volume of the fish:
   Volume = Mass / Body Density = 85.0 kg / 1015 kg/m³ = 0.0837 m³
2. Calculate the weight of the water displaced:
   Weight of Water Displaced = Volume * Density of Salt Water = 0.0837 m³ * 1025 kg/m³ = 85.79 kg
3. Calculate the force the grouper must exert:
   Force = Weight of Water Displaced = 85.79 kg * 9.8 m/s² = 840.44 N

Therefore, the grouper must exert a force of 840.44 N to stay submerged in salt water.