Question

A bathysphere used for deep-sea exploration has a radius of 1.50 m and a mass of 1.23 ✕ 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 1.20 m/s, when the resistive force on it is 1095 N in the upward direction. Take 1.03 ✕ 103 kg/m3 as the density of seawater.

Answer 1

Given radius of bathysphere , = 1.5 m

so volume V =

V=

V= 14.14 m³

Buoyant Force experienced =

B = 1.03*10³ *14.14 *9.81

B = 142874.8 N

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Since the submarine is descending with constant velocity ,acceleration =0 m/s²

Net Force =ma =0

There are 3 forces acting on submarine: Buoyant force acting upwards ,

Resistive Force acting upwards and

Weight of the Submarine acting downwards

So Net Force =0

Mg - Buoyant Force -Resistive Force =0

Mg = Buoyant Force +Resistive Force

Mg= 142874.8 + 1095

M = 143969.8/9.81

M = 14675.82 kg

This mass is sum of mass of submarine and mass of water

m_s +m_w =14675.82

m_w =14675.82 -m_s

m_w =14675.82 -1.23*10⁴

m_w =2375.82 kg

ANSWER: m_w =2375.82 kg

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