Question

The greatest ocean depths on Earth are found in the Marianas Trench near the Philippines. Calculate the pressure due to the ocean at the bottom of this trench, given its depth is 11.0km and assuming the density of seawater is constant all the way down.

1. 1.08×10⁸ Pa
2. 1.08×10⁹ Pa
3. 1.08×10¹⁰ Pa
4. 1.08×10¹¹ Pa

Answer 1

The pressure at the bottom of the Marianas Trench is calculated using the formula P = hpg, resulting in a pressure of 1.08×10¸ pascals (Pa).

Step-by-step explanation:

To calculate the pressure due to the ocean at the bottom of the Marianas Trench, the formula used is P = hpg, where P is the pressure, h is the depth of the water, ρ (rho) is the density of seawater, and g is the acceleration due to gravity. The SI unit of pressure is pascals (Pa), and since hpg yields units of N/m², which is equivalent to Pa, we can confirm that the SI unit of hpg is indeed N/m².

Given a depth h of 11.0 km (or 11,000 m), a density of seawater ρ of approximately 1025 kg/m³, and the acceleration due to gravity g as 9.81 m/s², we can calculate the pressure at the bottom of the trench as follows:

P = hρg = (11,000 m)(1025 kg/m³)(9.81 m/s²) = 1.101×10³ kg/(ms²) × 9.81 m/s² = 1.08×10¸ Pa.

The pressure due to the ocean at the bottom of the Marianas Trench is therefore 1.08×10¸ Pa, which corresponds to option 1 in the multiple-choice question.