Problem Solving and Application Flashcards

A submarine is operating at a depth of 200 meters in seawater. Assuming the density of seawater is approximately 1025 kg/m³ and the acceleration due to gravity (g) is 10 m/s², what is the gauge pressure exerted on the submarine's hull?

Answer: 2,050,000 Pa

The gauge pressure at a certain depth in a fluid is calculated using the formula P = ρgh, where P is pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth. Plugging in the values: P = (1025 kg/m³) * (10 m/s²) * (200 m) = 2,050,000 Pa.

A piece of electronic equipment on a naval ship is rated to operate at 120 V and draws a current of 2.5 A. How much power does this equipment consume during operation?

Answer: 300 W

Electrical power (P) is calculated by multiplying voltage (V) by current (I), using the formula P = V * I. In this scenario, P = 120 V * 2.5 A = 300 W.

A ship's diesel engine takes in 8,000 kJ of heat from fuel combustion and rejects 5,000 kJ of waste heat to the seawater coolant system during one cycle. What is the thermal efficiency of this engine?

Answer: 37.5%

Thermal efficiency (η) is the ratio of the net work done (W) to the heat input (Q_H). The work done is the difference between the heat input and the heat rejected (W = Q_H - Q_C). So, W = 8,000 kJ - 5,000 kJ = 3,000 kJ. The efficiency is then η = (W / Q_H) * 100% = (3,000 kJ / 8,000 kJ) * 100% = 0.375 * 100% = 37.5%.

A technician needs to prepare a 500 mL cleaning solution with a 2.0 Molar (M) concentration of sodium hydroxide (NaOH). Given that the molar mass of NaOH is 40.0 g/mol, what mass of NaOH is required?

Answer: 40.0 g

First, calculate the number of moles needed using the formula: Moles = Molarity × Volume (in Liters). Convert 500 mL to 0.5 L. Moles = 2.0 mol/L * 0.5 L = 1.0 mol. Then, convert moles to mass using the formula: Mass = Moles × Molar Mass. Mass = 1.0 mol * 40.0 g/mol = 40.0 g.

In a nuclear fission reaction within a reactor, 5.0 x 10⁻¹² kg of mass is converted directly into energy. Using Einstein's mass-energy equivalence principle (E=mc²), calculate the amount of energy released. (Use c ≈ 3.0 x 10⁸ m/s).

Answer: 4.5 x 10⁵ J

The energy (E) released is calculated using the formula E = mc², where m is the mass defect and c is the speed of light. E = (5.0 x 10⁻¹² kg) * (3.0 x 10⁸ m/s)². First, square the speed of light: (3.0 x 10⁸)² = 9.0 x 10¹⁶. Then, multiply by the mass: E = (5.0 x 10⁻¹²) * (9.0 x 10¹⁶) = 45 x 10⁴ J, which is properly written as 4.5 x 10⁵ J.

A winch on a ship's deck lifts a 500 kg crate of supplies from the pier to a height of 20 meters in 40 seconds. What is the average power output of the winch, ignoring friction? (Use g ≈ 10 m/s²).

Answer: 2,500 W

Power is the rate at which work is done (Power = Work / time). First, calculate the work done against gravity: Work = Force × distance = (mass × g) × height. Work = (500 kg × 10 m/s²) × 20 m = 5,000 N × 20 m = 100,000 Joules. Then, calculate the power: Power = 100,000 J / 40 s = 2,500 Watts.