Question

A bathysphere used for deep-sea exploration has a radius of 1.50 m and a mass of 1.19 104 kg. In order 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 1.40 m/s, when the resistive force on it is 1105 N in the upward direction. Take 1.03 103 kg/m3 as the density of seawater. answer in kg

Answer 1

Answer:

m = 2,776.95 kg

Explanation:

given,

radius = 1.5 m

mass = 1.19 x 10⁴ Kg

constant speed, v = 1.4 m/s

Resistive force = 1105 N

density of sea water = 1.03 x 10³ kg/m³

Volume of vessel,

$v=\dfrac{4}{3}\pi r^3$

$v=\dfrac{4}{3}\pi\times 1.5^3$

v = 14.14 m³

Upthrust,

U = ρ g V

U = 1030 x 9.8 x 14.14

U  = 142729.16 N  

Since the vessel is moving at a constant speed, the resultant force on it should equal zero.

downward acting forces = upward acting forces

Mg = U + resistive force

M x 9.8 = (142729.16+1105)

M=14676.95 Kg

Mass of water,

m = M - mass of vessel  

m = 14676.95 Kg- 11,900 kg  

m = 2,776.95 kg