Imagine a particular exoplanet covered in an ocean of liquid methane. At the surface of the ocean, the acceleration of gravity is 6.20 m/s2, and atmospheric pressure is 7.00 ✕ 104 Pa. The atmospheric temperature and pressure on this planet causes the density of the liquid methane ocean to be 415 kg/m3. (a) What force (in N) is exerted by the atmosphere on a disk-shaped region 2.00 m in radius at the surface of the ocean? N (b) What is the weight, on this exoplanet, of a 10.0 m deep cylindrical column of methane with radius 2.00 m? (Enter your answer in N.) N (c) What is the pressure (in Pa) at a depth of 10.0 m in the methane ocean?

Question

Gracelyn Peters

Physics

18 March, 07:43

Imagine a particular exoplanet covered in an ocean of liquid methane. At the surface of the ocean, the acceleration of gravity is 6.20 m/s2, and atmospheric pressure is 7.00 ✕ 104 Pa. The atmospheric temperature and pressure on this planet causes the density of the liquid methane ocean to be 415 kg/m3. (a) What force (in N) is exerted by the atmosphere on a disk-shaped region 2.00 m in radius at the surface of the ocean? N (b) What is the weight, on this exoplanet, of a 10.0 m deep cylindrical column of methane with radius 2.00 m? (Enter your answer in N.) N (c) What is the pressure (in Pa) at a depth of 10.0 m in the methane ocean?

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Answers (1)

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Michelle Chung · Answer 1

Atmospheric pressure = 7 x 10⁴ Pa

force on a disk-shaped region 2.00 m in radius at the surface of the ocean due to atmosphere = pressure x area

= 7 x 10⁴ x 3.14 x 2 x 2

= 87.92 x 10⁴ N

b)

weight, on this exoplanet, of a 10.0 m deep cylindrical column of methane with radius 2.00 m

Pressure x area

height x density x acceleration of gravity x π r²

= 10 x 415 x 6.2 x 3.14 x 2 x 2

=323168.8 N

c) Pressure at a depth of 10 m

atmospheric pressure + pressure due to liquid column

= 7 x 10⁴ + 10 x 415 x 6.2 (hρg)

= 7 x 10⁴ + 10 x 415 x 6.2

(7 + 2.57) x 10⁴ Pa

9.57 x 10⁴ Pa