Question

Водоизмещение танкера равно 400 тысяч тонн. В порт танкер прибыл с полной загрузкой. После частичной разгрузки танкера его осадка в уменьшилась на 800 см. Определите массу нефти, оставшейся на танкере, если площадь сечения танкера на уровне воды равна 10тысячм2, а вес сухого танкера 200 тысяч тонн. Плотность воды принять равной 1000кг/м3. Показать ход решения задачи и формулы. Ответ дать в тысячах тонн.

Answer 1

Дано
V*p=4*10^8 м^3
Δh=8 м
S=10^4 м^2
mt=2*10^8 кг
p=1000 кг/м^3
_____________________
Составим уравнение для полного танкера и найдем массу нефти
(mt+m1)*g=p*g*V
mt+m1=p*V=4*10^8=4*10^8
m1=4*10^8-mt=4*10^8-2*10^8=2*10^8 кг=200 тысяч тонн
Запишем уравнение для танкера с отгруженной нефтью
(mt+m2)*g=p*g*(V-S*Δh)
(mt+m2)=p*V-S*Δh*p
(mt+m2)=4*10^8-10^4*8*1000)=3.2*10^8
m2=3.2*10^8-2*10^8=1,2*10^8 кг=120 тыс. тонн
найдем массу слитого топлива
ms=m1-m2=2*10^8-1,2*10^8=80 тыс тонн

Answer 2

Problem Analysis

We are given the displacement of a tanker, the change in its draft after partial unloading, the cross-sectional area of the tanker at the water level, the weight of the empty tanker, and the density of water. We need to determine the mass of the remaining oil on the tanker.

Solution

To solve this problem, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

The buoyant force can be calculated using the formula:

Buoyant force = Weight of the fluid displaced

The weight of the fluid displaced can be calculated using the formula:

Weight of the fluid displaced = Density of the fluid * Volume of the fluid displaced

In this case, the fluid is water, and the volume of the fluid displaced is equal to the change in draft of the tanker.

Let's calculate the volume of the fluid displaced:

Volume of the fluid displaced = Cross-sectional area of the tanker at the water level * Change in draft of the tanker

Now, we can calculate the buoyant force:

Buoyant force = Density of water * Volume of the fluid displaced

Since the buoyant force is equal to the weight of the remaining oil on the tanker, we can equate the two:

Weight of the remaining oil = Buoyant force

Let's substitute the values given in the problem and calculate the weight of the remaining oil.

Calculation

Given: - Displacement of the tanker = 400,000 tons - Change in draft of the tanker = 800 cm - Cross-sectional area of the tanker at the water level = 10,000 m^2 - Weight of the empty tanker = 200,000 tons - Density of water = 1000 kg/m^3

First, let's convert the change in draft from centimeters to meters: Change in draft of the tanker = 800 cm = 8 m

Now, let's calculate the volume of the fluid displaced: Volume of the fluid displaced = Cross-sectional area of the tanker at the water level * Change in draft of the tanker Volume of the fluid displaced = 10,000 m^2 * 8 m = 80,000 m^3

Next, let's calculate the buoyant force: Buoyant force = Density of water * Volume of the fluid displaced Buoyant force = 1000 kg/m^3 * 80,000 m^3 = 80,000,000 kg

Finally, let's convert the buoyant force from kilograms to tons: Weight of the remaining oil = Buoyant force = 80,000,000 kg = 80,000 tons

Therefore, the mass of the remaining oil on the tanker is 80,000 tons.

Answer

The mass of the remaining oil on the tanker is 80,000 tons.