Question

A scuba tank, when fully submerged, displaces 16.4 L of seawater. The tank itself has a mass of 14.1 kg and, when "full," contains 4.76 kg of air.

1_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).

Express your answer with the appropriate units.

2_

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).

Express your answer with the appropriate units.

Answer 1

The buoyant force is the weight of the water it displaces
Density = mass/Volume so Volume*Density = mass and weight = g*Volume*Density
We have to convert liters to m³
One of the nicest things about MKS is 1ml = 1cc = 1cm³
16.4L*1000cm³/L * (1m/100cm)³ = 0.0164m³
Weight of water displaced = 9.8*0.0164*1025 = 164.738N
The weight of the tank = (14.1+4.76)*9.8 = 184.828N
184.828-164.738

= 20.09N <---------- 1

The weight of the tank without air = 14.1*9.8 = 138.18N
164.738-138.18= 26.558N <------------ 2