Question

A spherical vessel used for deep-sea exploration has a radius of 1.50 m and a mass of 1.20 × 104 kg. To dive, the vessel takes on mass in the form of seawater. Determine the mass the vessel must take on if it is to descend at a constant speed of 1.20 m/s, when the resistive force on it is 1100 N in the upward direction. The density of seawater is equal to 1.03 × 103 kg/m3.

Answer 1

Σ𝐹𝑦=𝑚𝑎𝑦=0−(1.20×104𝑘𝑔+𝑚)𝑔+𝑝𝑤𝑔𝑉+1100𝑁=0
Where 𝑚 is the mass of the added water and 𝑣 is the sphere’s volume. 1.20×104𝑘𝑔+𝑚=1.03×103[43𝜋(1.50)3]+1100𝑁9.8𝑚/𝑠2=2.67×103𝑘𝑔