A bathysphere used for deep-sea exploration has a radius of 1.51 m and a mass of

Question

A bathysphere used for deep-sea exploration has a radius of 1.51 m and a mass of 1.22 104 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 1.00 m/s, when the resistive force on it is 1097 N in the upward direction. The density of seawater is 1.03 103 kg/m3.

I got 2473.16 kg and it said "Your response differs from the correct answer by more than 10%."

thank you. please show me step by step so i can understand!

Explanation / Answer

Its volume is 4/3 r3=14.42m3

The mass of water corresponding to that volume is (1.03 x103kg/m3)(14.42m3)=1.4854x104kg

The difference in the mass of the water and the mass of the bathysphere is the amount of mass required to sink the sphere.

1.4854x104kg-1.22x104kg=2.654x103kg

the mass to force conversion is

F=ma

F=2.654x103kg x 9.8m/s2

F=2.6009x104N

The problem reads that there is a resistive force of 1097N in the upward direction

add that to the amount of force required to sink and divide by 9.8

2.7106x104N

F/a=m

2.7106x104/9.8 = 2.765x104kg

See if that works

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