Question

Джек Доусон пытается сбежать из трюма тонущего Титаника. Палуба, на которой он находится, уже погрузилась на 4 метра под воду. С какой силой Джек должен прижимать водонепроницаемую дверь, чтобы поток воды не смог её открыть? Высота двери 2м, ширина - 80 см, плотность солёной воды - 1030 кг/м3​ помогите пожалуйста

Answer 1

Ответ: Джек должен прижимать водонепроницаемую дверь, чтобы поток воды не смог её открыть, с силой 64,6 кН.

Объяснение:

ДАНО:

h = 4 м

a = 2 м

b = 80 см = 0,8 м

ρ = 1030 кг/м³

g = 9,8 Н/кг

F - ?

РЕШЕНИЕ:

Смоделируем данную ситуацию для решения задачи. Столб жидкости высотой 4 м давит на  дверь. Воспользуемся формулой давления столба жидкости на дно сосуда:

р = F/S, где F - сила, с которой жидкость действует на дно сосуда; S - площадь дна сосуда.

По условию задачи сила которую должен применить Джек относительно двери, чтобы поток не смог ее открыть должна быть равна силе F. Выразим из предыдущей формулы силу:

F = p · S.

р - давление создаваемое столбом жидкости на дверь, вычисляется по формуле p = ρgh.

S - площадь двери, найдем как произведение ее высоты и ширины S = a · b.

Тогда итоговая формула будет выглядеть так:

F = ρgh · ab

F = 1030 · 9,8 · 4 · 2 · 0,8 = 64602 Н

F = 64,6 кН.

Answer 2

To calculate the force that Jack needs to apply to the watertight door to prevent it from being opened by the water flow, we can use Archimedes' principle and the concept of pressure.

Archimedes' Principle:

Archimedes' principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.

Pressure:

Pressure is defined as the force per unit area. In this case, we can calculate the pressure exerted by the water on the door.

To calculate the force that Jack needs to apply, we can follow these steps:

1. Calculate the weight of the water that the door displaces. 2. Calculate the pressure exerted by the water on the door. 3. Calculate the force required to counteract the pressure.

Step 1: Calculate the weight of the water that the door displaces.

The weight of the water displaced by the door is equal to the weight of the volume of water that the door occupies. We can calculate the volume using the dimensions of the door.

The volume of the door can be calculated as follows: Volume = height * width * depth

Given: - Height of the door = 2 m - Width of the door = 80 cm = 0.8 m - Depth of the water = 4 m (since the deck has already submerged by 4 meters)

Volume of the door = 2 m * 0.8 m * 4 m = 6.4 m^3

The weight of the water displaced by the door can be calculated using the density of saltwater, which is 1030 kg/m^3.

Weight of the water displaced = Volume * Density Weight of the water displaced = 6.4 m^3 * 1030 kg/m^3 = 6,592 kg

Step 2: Calculate the pressure exerted by the water on the door.

Pressure is defined as force per unit area. In this case, the force is the weight of the water displaced, and the area is the area of the door.

The area of the door can be calculated as follows: Area = height * width

Given: - Height of the door = 2 m - Width of the door = 80 cm = 0.8 m

Area of the door = 2 m * 0.8 m = 1.6 m^2

The pressure exerted by the water on the door can be calculated using the formula: Pressure = Force / Area

Pressure = (Weight of the water displaced) / (Area of the door) Pressure = 6,592 kg / 1.6 m^2 = 4,120 Pa (approximately)

Step 3: Calculate the force required to counteract the pressure.

To counteract the pressure exerted by the water, Jack needs to apply an equal and opposite force.

Force = Pressure * Area

Given: - Area of the door = 1.6 m^2 - Pressure = 4,120 Pa

Force = 4,120 Pa * 1.6 m^2 = 6,592 N

Therefore, Jack needs to apply a force of approximately 6,592 Newtons to the watertight door to prevent the water flow from opening it.

Please note that this calculation assumes ideal conditions and does not take into account other factors such as water turbulence or the structural integrity of the door.