Question

The Mariana Trench, in the Pacific Ocean, is about 11 km deep. If atmospheric pressure at sea level is 1.01 × 10^5 Pa and the density of sea water is 1025 kg/m3 , how much pressure would a submarine need to be able to withstand to reach this depth? The acceleration of gravity is 9.81 m/s 2 . Answer in units of Pa.

Answer 1

The submarine would need to withstand a pressure of approximately 114.35 Megapascals (MPa) to reach the bottom of the Mariana Trench, calculated using the formula for pressure in a fluid.

Step-by-step explanation:

To calculate the pressure a submarine would need to withstand to reach the bottom of the Mariana Trench, we use the formula P = P0 + ρgh, where P is the total pressure, P0 is the atmospheric pressure at sea level, ρ is the density of seawater, g is the acceleration due to gravity, and h is the depth. Given that P0 is 1.01 × 105 Pa (atmospheric pressure at sea level), ρ is 1025 kg/m3 (density of seawater), g is 9.81 m/s2, and h is 11 km (11000 m), we can calculate:

P = 1.01 × 105 Pa + (1025 kg/m3 × 9.81 m/s2 × 11000 m)

P = 1.01 × 105 Pa + 113278500 Pa

P = 114348500 Pa

The pressure at the bottom of the Mariana Trench is approximately 114.35 Megapascals (MPa), so the submarine needs to withstand at least this pressure.

Answer 2

To calculate the pressure at the depth of the Mariana Trench, use the pressure equation P = ρgh + P0. With the given constants, the pressure a submarine must withstand to reach this depth is approximately 1.118 × 10^8 Pa.

Step-by-step explanation:

To calculate the pressure that a submarine would need to withstand at the depth of the Mariana Trench, one can use the equation for pressure due to a fluid column, which is P = ρgh + P0, where ρ is the density of the fluid (sea water in this case), g is the acceleration due to gravity, h is the height (or depth) of the fluid column, and P0 is the atmospheric pressure at the surface level.

Given the density of seawater (ρ) as 1025 kg/m3, acceleration due to gravity (g) as 9.81 m/s2, depth (h) of the Mariana Trench as 11,000 m (since 1 km = 1000 m), and the atmospheric pressure at sea level (P0) as 1.01 × 105 Pa, we can calculate the pressure using these values.

The pressure due to the ocean at the given depth is:

P = 1025 kg/m3 × 9.81 m/s2 × 11,000 m + 1.01 × 105 Pa

P = 1.117 × 108 Pa + 1.01 × 105 Pa
= 1.118 × 108 Pa (approx)

A submarine would need to be able to withstand a pressure of approximately 1.118 × 108 Pa to reach the bottom of the Mariana Trench.