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/m^3. 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?
The Correct Answer and Explanation is:
Correct Answer:
Given:
- Mass of bull shark, m=92 kgm = 92 \, \text{kg}m=92kg
- Density of shark, ρshark=1040 kg/m3\rho_{\text{shark}} = 1040 \, \text{kg/m}^3ρshark=1040kg/m3
- Density of seawater, ρsea=1025 kg/m3\rho_{\text{sea}} = 1025 \, \text{kg/m}^3ρsea=1025kg/m3
- Density of freshwater, ρfresh=1000 kg/m3\rho_{\text{fresh}} = 1000 \, \text{kg/m}^3ρfresh=1000kg/m3
- Acceleration due to gravity, g=9.81 m/s2g = 9.81 \, \text{m/s}^2g=9.81m/s2
Step 1: Find volume of the shark
V=mρshark=921040=0.0885 m3V = \frac{m}{\rho_{\text{shark}}} = \frac{92}{1040} = 0.0885 \, \text{m}^3V=ρsharkm=104092=0.0885m3
Step 2: Compute buoyant force in seawater and freshwater
(a) In seawater: Fbuoy, sea=ρsea⋅V⋅g=1025⋅0.0885⋅9.81=891.5 NF_{\text{buoy, sea}} = \rho_{\text{sea}} \cdot V \cdot g = 1025 \cdot 0.0885 \cdot 9.81 = 891.5 \, \text{N}Fbuoy, sea=ρsea⋅V⋅g=1025⋅0.0885⋅9.81=891.5N
(b) In freshwater: Fbuoy, fresh=ρfresh⋅V⋅g=1000⋅0.0885⋅9.81=868.8 NF_{\text{buoy, fresh}} = \rho_{\text{fresh}} \cdot V \cdot g = 1000 \cdot 0.0885 \cdot 9.81 = 868.8 \, \text{N}Fbuoy, fresh=ρfresh⋅V⋅g=1000⋅0.0885⋅9.81=868.8N
Step 3: Compute weight of the shark
W=m⋅g=92⋅9.81=902.5 NW = m \cdot g = 92 \cdot 9.81 = 902.5 \, \text{N}W=m⋅g=92⋅9.81=902.5N
Step 4: Find required lift force
(a) In seawater: Flift, sea=W−Fbuoy, sea=902.5−891.5=11.0 NF_{\text{lift, sea}} = W – F_{\text{buoy, sea}} = 902.5 – 891.5 = 11.0 \, \text{N}Flift, sea=W−Fbuoy, sea=902.5−891.5=11.0N
(b) In freshwater: Flift, fresh=902.5−868.8=33.7 NF_{\text{lift, fresh}} = 902.5 – 868.8 = 33.7 \, \text{N}Flift, fresh=902.5−868.8=33.7N
Final Answers:
- Lift force required in seawater: 11.0 N
- Lift force required in freshwater: 33.7 N
Explanation
Sharks are generally negatively buoyant, which means they sink in water unless they actively maintain their position. Unlike bony fish that have swim bladders to regulate buoyancy, sharks rely on continuous swimming and hydrodynamic lift generated by their fins to stay afloat.
To understand the lift required, we begin by calculating the shark’s volume using its mass and density. A shark with a mass of 92 kg and a density of 1040 kg/m³ has a volume of about 0.0885 cubic meters.
Next, we calculate the buoyant force the shark experiences in different water types. Buoyant force depends on the volume of displaced water, the density of that water, and gravity. In seawater, which is denser than the shark (1025 kg/m³), the buoyant force is slightly less than the shark’s weight, resulting in a small net downward force. Specifically, the shark weighs 902.5 newtons, and the buoyant force from seawater is 891.5 newtons, so it needs 11.0 newtons of lift to stay at the same depth.
In freshwater, the situation changes. Water is less dense (1000 kg/m³), so the buoyant force decreases to 868.8 newtons. The lift needed increases to 33.7 newtons because the water supports the shark less than seawater does.
This illustrates how the environment affects shark physiology and behavior. Sharks like the bull shark, which can swim in both salt and freshwater, must adjust their swimming patterns and fin movements to generate additional lift in rivers compared to oceans. This adaptation is essential for maintaining depth and conserving energy during movement.
