Question

A scuba tank, when fully submerged, displaces15.7 Lof seawater. The tank itself has a mass of13.5kgand, when "full," contains 3.20kgof air. The density of seawater is 1025 kg/m3. Assume that only its weight and the buoyant force act on the tank.

Part A
Determine the magnitude of the net force on the fully submerged tank at the beginning of a dive (when it is full of air).
Part B
Determine the direction of the net force on the fully submerged tank at the beginning of a dive (when it is full of air).
Part C
Determine the magnitude of the net force on the fully submerged tank at the end of a dive (when it no longer contains any air).
Part D
Determine thedirection of the net force on the fully submerged tank at the end of a dive (when it no longer contains any air).


Upward or Downward?

Answer 1

The net force on a fully submerged scuba tank can be found using Archimedes' principle to compare the buoyant force and the weight of the tank with and without air. The direction of the net force depends on whether the buoyant force exceeds the total weight of the tank.

Step-by-step explanation:

To determine the magnitude of the net force on the fully submerged scuba tank, we'll use Archimedes' principle, which tells us that the buoyant force acting on a submerged object is equal to the weight of the fluid that the object displaces. We calculate this force using the density of seawater and the volume of water displaced by the tank.

Part A

The buoyant force can be calculated with the formula: Buoyant Force = Volume displaced × Density of fluid × Gravity. Substituting the given values, we get Buoyant Force = 15.7 L × 1025 kg/m³ × 9.8 m/s² (Note: 1 L = 0.001 m³). To find the net force, we subtract the weight of the tank and the air from the buoyant force.

Part B

The direction of the net force depends on whether the buoyant force is greater than the combined weight of the tank and the air inside it. If it is greater, the net force is upward, otherwise downward.

Part C

At the end of a dive, the tank no longer contains any air. The weight of the tank remains the same, so we again subtract the weight of the tank from the buoyant force to calculate the net force.

Part D

The direction of the net force is determined by comparing the buoyant force to the weight of the tank, similar to Part B.