Question

Sharks are generally negatively buoyant; the upward buoyant force is less than the weight force. This is one reason sharks tend to swim continuously; water moving past their fins causes a lift force that keeps sharks from sinking. A 92 kg bull shark has a density of 1040 kg/m3. What lift force must the shark's fins provide if the shark is swimming in seawater? Bull sharks often swim into freshwater rivers. What lift force is required in a river?

Answer 1

Answer:

8.67807 N

34.7123 N

Explanation:

m = Mass of shark = 92 kg

$\rho_{se}$ = Density of seawater = 1030 kg/m³

$\rho_{f}$ = Density of freshwater = 1000 kg/m³

$\rho_{sh}$ = Density of shark = 1040 kg/m³

g = Acceleration due to gravity = 9.81 m/s²

Net force on the fin is (seawater)

$F_n=mg-V_s\rho_{se}g\\\Rightarrow F_n=mg-\frac{m}{\rho_{sh}}\rho_{se}g\\\Rightarrow F_n=92\times 9.81-\frac{92}{1040}\times 1030\times 9.81\\\Rightarrow F_n=8.67807\ N$

The lift force required in seawater is 8.67807 N

Net force on the fin is (freshwater)

$F_n=mg-V_s\rho_{f}g\\\Rightarrow F_n=mg-\frac{m}{\rho_{sh}}\rho_{f}g\\\Rightarrow F_n=92\times 9.81-\frac{92}{1040}\times 1000\times 9.81\\\Rightarrow F_n=34.7123\ N$

The lift force required in a river is 34.7123 N