. A bathysphere used for deep-sea exploration has a radius of 1.50 m and a mass of 1.20 104 kg. To dive, this submarine takes on mass in the form of seawater. 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 1 100 N in the upward direction. Take 1.03 103 kg/m3 as the density of seawater.

In this exercise we have to use fluid knowledge to calculate the mass immersed in water, so we will find that:

Given that:

The volume of the bathysphere can be calculated using

The Bouyant force can be calculated using:

Weight of the bathysphere can be calculated by:

The net positive buoyant using resolving:

So we can say that:

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Explanation:

Given that,

Bathysphere radius

r = 1.5m

Mass of bathysphere

M = 1.2 × 10⁴ kg

Constant speed of descending.

v = 1.2m/s

Resistive force

Fr = 1100N upward direction

Density of water

ρ = 1.03 × 10³kg/m³

The volume of the bathysphere can be calculated using

V = 4πr³ / 3

V = 4π × 1.5³ / 3

V = 14.14 m³

The Bouyant force can be calculated using

Fb = ρgV

Fb = 1.03 × 10³ × 9.81 × 14.14

Fb = 142,846.18 N

Buoyant force is acting upward

Weight of the bathysphere

W = mg

W = 1.2 × 10⁴ × 9.81

W = 117,720 N

Weight is acting downward

The net positive buoyant using resolving

Fb+ = Fb — W

Fb+ = 142,846.18 — 117,720

Fb+ = 25,126.18 N

The force acting downward is the weight of the submarine and it is equal to the positive buoyant force and the resistive force

W = Fb+ + Fr

W = 25,126.18 + 1100

W = 26,226.18

mg = 26,226.18

m = 26,226.18 / 9.81

m = 2673.4kg

Mass of submarine is 2673.4kg

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find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2