Question

Some fish have a density slightly less than that of water and must exert a force to stay submerged. What force must an 85 keg grouper exert to stay submerged in salt water if it’s body density is 1015 kg/m cubed

Answer 1

An 85.0-kg grouper with a body density of 1015 kg/m³ must exert a force of 8.89 N to stay submerged in salt water, compensating for the buoyant force that causes it to float.

Step-by-step explanation:

To calculate the force that an 85.0-kg grouper must exert to stay submerged in salt water, we need to use the concept of buoyancy from Archimedes' Principle.

The buoyant force on the grouper is equal to the weight of the volume of water displaced by the fish.

Since the fish's density is slightly less than the density of salt water, the buoyancy will cause the fish to float, and the fish must swim downwards to stay submerged.

First, we calculate the volume of the grouper using its mass and density:

V = m / ρ

V = 85.0 kg / 1015 kg/m³

V = 0.08374 m³

The buoyant force can be calculated using the volume and the density of salt water (typically around 1027 kg/m³):

Fb = V × ρwater × g

Fb = 0.08374 m³ × 1027 kg/m³ × 9.81 m/s²

Fb = 842.74 N

Now, we need to calculate the weight of the grouper:

W = m × g

W = 85 kg × 9.81 m/s²

W = 833.85 N

To stay submerged, the grouper must exert a force (through swimming) equal to the difference between the buoyant force and its weight:

Fexert = Fb - W

Fexert = 842.74 N - 833.85 N

Fexert = 8.89 N

The grouper must exert an upward force of 8.89 N to stay submerged.