Question

Полый цилиндр плавает в керосине плотности ρ = 800кг/м3. Для того, чтобы этот цилиндр плавал с такой же глубиной погружения в воде, в него следует поместить груз массой m = 100кг. Определите массу цилиндра.

Answer 1

Плотность керосина 800кг на метр в кубе (p1)
Плотность воды 1000 кг на метр в кубе (p2)
Если он плавает значит Fт=Fa
Fт=m1g
m1- масса цилиндра
Fа=p1gV

Запишем тоже самое, но для воды
Fт=Fа
Fт=(m1+100)*g
Fa=p2gV

Объем цилиндра не изменится, плотности нам известны, можем разделить первое на второе
m1g/(m1+100)*g=p1gV/p2gV   Сократим на g
m1/m1+100=p1V/p2V сократим вторую часть на V
m1/m1+100=p1/p2
m1/m1+100=0,8
0.8m1+80=m1
80=,m1-0.8m1
80=0,2m1
m1=400 кг

Ответ 400

Answer 2

Problem Analysis

We are given a cylindrical object that is floating in kerosene with a density of ρ = 800 kg/m^3. To make the cylinder float at the same depth in water, we need to add a weight with a mass of m = 100 kg. We need to determine the mass of the cylinder.

Solution

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

Let's denote the mass of the cylinder as M and the volume of the cylinder as V. The buoyant force acting on the cylinder in kerosene is given by:

Buoyant force in kerosene = Weight of kerosene displaced by the cylinder

The weight of the kerosene displaced by the cylinder can be calculated using the formula:

Weight of kerosene displaced = Density of kerosene * Volume of cylinder * Acceleration due to gravity

The buoyant force acting on the cylinder in water is given by:

Buoyant force in water = Weight of water displaced by the cylinder

The weight of the water displaced by the cylinder can be calculated using the formula:

Weight of water displaced = Density of water * Volume of cylinder * Acceleration due to gravity

Since the cylinder floats at the same depth in both kerosene and water, the buoyant forces in kerosene and water are equal. Therefore, we can equate the two expressions for the buoyant force:

Density of kerosene * Volume of cylinder * Acceleration due to gravity = Density of water * Volume of cylinder * Acceleration due to gravity

We can cancel out the common terms and solve for the volume of the cylinder:

Density of kerosene = Density of water

Volume of cylinder = (Density of water / Density of kerosene) * Volume of cylinder

Now, we can substitute the given values into the equation:

ρ_kerosene = 800 kg/m^3

ρ_water = 1000 kg/m^3 (density of water)

m = 100 kg (mass of the weight added to the cylinder)

Substituting these values into the equation, we get:

Volume of cylinder = (1000 kg/m^3 / 800 kg/m^3) * Volume of cylinder

Simplifying the equation, we find:

1.25 * Volume of cylinder = Volume of cylinder

Since the volume of the cylinder is the same on both sides of the equation, we can conclude that the coefficient 1.25 must be equal to 1. Therefore, the density of kerosene must be equal to the density of water.

Using this information, we can determine that the mass of the cylinder is equal to the mass of the weight added to the cylinder:

Mass of cylinder = Mass of weight = 100 kg

Therefore, the mass of the cylinder is 100 kg.

Answer

The mass of the cylinder is 100 kg.