jenha14
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A bathysphere used for deep-sea exploration has a radius of 1.52 m and a mass of 1.20 x 104 kg. To dive, this submarine takes on mass in the form of sea water. Determine the amount of mass that the submarine must take on if it is to descend at a constant speed of 1.10 m/s, when the resistive force on it is 1102 N in the upward direction. The density of seawater is 1.03 x 103 kg/m3.
ATTEMPT AT SOLUTION
When the bathysphere descends at constant velocity the sum on the force acting on it equals zero:
m · a = Σ F = 0
<=>
F_gravity - F_buoyancy - F_resistive = 0
<=>
m·g - ρ_water·V_sphere·g - F_resistive = 0
<=>
m·g - ρ_water·(4/3)·π·(R_sphere)³·g - F_resistive = 0
ATTEMPT AT SOLUTION
When the bathysphere descends at constant velocity the sum on the force acting on it equals zero:
m · a = Σ F = 0
<=>
F_gravity - F_buoyancy - F_resistive = 0
<=>
m·g - ρ_water·V_sphere·g - F_resistive = 0
<=>
m·g - ρ_water·(4/3)·π·(R_sphere)³·g - F_resistive = 0