A bathysphere used for deep sea exploration has a radius of 1.50 m and a mass of 1.20 × 104 kg. In order to dive, the sphere takes on mass in the form of sea water. a) Determine the mass the bathysphere must take on so that it can descend at a constant speed of 1.20 m/s when the resistive force on it is 1 100 N upward. The density of sea water is 1.03 × 103 kg/m3.

Question

A bathysphere used for deep sea exploration has a radius of 1.50 m and a mass of 1.20 × 104 kg. In order to dive, the sphere takes on mass in the form of sea water.      a)  Determine the mass the bathysphere must take on so that it can descend at a constant speed of 1.20 m/s when the resistive force on it is 1 100 N upward. The density of sea water is 1.03 × 103 kg/m3.

Damon · Accepted Answer

volume = (4/3) pi r^3 = (4/3) pi (1.5)^3
= 14.1 m^3
buoyant force = rho g V = 1.03*10^3 * 9.8 * 14.1 = 142,700 N

weight down = 1.2*10^4*9.8 = 117,600 N

net positive buoyancy = 142700-117600 = 25,100 N

Force down - 25,100 N = 1,100 N

Force down = 26,200 N
mass = 26,200/9.8 = 2673 kg