Final answer:
To stay submerged, a 68.0 kg grouper with a body density of 1017 kg/m3 must exert an additional force of approximately 6.8 N, which is the difference between the buoyant force and its weight in saltwater.
Step-by-step explanation:
The question is asking to calculate the force a grouper fish must exert to stay submerged in water, given its density and mass.
To find the force, we first calculate the weight of the water displaced by the fish using Archimedes' principle. The buoyant force is equal to the weight of the water displaced, which we can calculate by finding the volume of the fish (using its density) and knowing the density of saltwater.
We then subtract the fish’s weight from the buoyant force to find the additional force needed to stay submerged.
First, we calculate the volume of the grouper: Volume = Mass / Density of grouper = 68.0 kg / 1017 kg/m³ ≈ 0.06687 m³. Second, assuming the density of saltwater to be approximately 1025 kg/m³, we calculate the buoyant force with the formula: Buoyant force = Volume × Density of saltwater × g ≈ 0.06687 m³ × 1025 kg/m³ × 9.80 m/s² ≈ 673.20 N. Finally, since the grouper’s weight (W = mg) is 68.0 kg × 9.80 m/s² = 666.40 N, the force it must exert to stay submerged is the difference between the buoyant force and its weight: Force exerted by grouper = Buoyant force - Weight ≈ 673.20 N - 666.40 N = 6.8 N.