Question

A scuba tank, when fully submerged, displaces 14.3L of seawater. The tank itself has a mass of 12.4 kg and, when "full," contains 2.91kg of air.
A) Assuming only a weight and buoyant force act, determine the net force (magnitude) on the fully submerged tank at the beginning of a dive (when it is full of air).
B) Assuming only a weight and buoyant force act, determine the net force (magnitude on the fully submerged tank at the end of a dive (when it no longer contains any air).

Answer 1

Answer:

A)   F = -9.8 N , B) F = 18.62 N

Explanation:

The Archimedes principle states that the thrust force is equal to the liquid farts dislodged by the body.

Let's apply Newton's equations

              F = B –W

         

Thrust force is

            B = ρ_water g V

Let's reduce volumes to the SI system

         V = 14.3 L (1 m³ / 1000 L) = 14.3 10⁻³ m³

A) Tank full of air

         m = 12.4 +2.9 = 15.3 kg

       

         F = ρ_water g V - mg

         F = 1 10³  9.8  14.3 10⁻³ - 15.3 9.8

         F = 140.14 -149.94

         F = -9.8 N

The negative sign indicates that the force is descending

B) Empty tank

         m = 12.4 kg

         F = 1 103 9.8 14.3 10⁻³ - 12.4 9.8

         F = 140.14 - 121.52

         F = 18.62 N

Force is up