Question

1.Металлический цилиндр объемом 200 см^3 полностью погружен в воду. Определите архимедову силу. 2.Чему равна архимедова сила, действующая на тело объёмом 2 м^3, на четверть объёма погруженное в воду. дам 50 баллов!

Answer 1

Решение:

1.

V = 200 см³ = 200·10⁻⁶ м³

ρ = 1000 кг/м³ - плотность воды

g = 10 Н/кг

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Архимедова сила       Fа = ρ · g · V = 1000 · 10 · 200·10⁻⁶ = 2 (H).

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2.

V = 2 м³

V₁ = V/4

ρ = 1000 кг/м³ - плотность воды

g = 10 Н/кг

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Архимедова сила       Fа = ρ · g · V₁ = 1000 · 10 · 2 : 4 = 5 000 (H) = 5 кН

Answer 2

Calculating Archimedes' Force

To calculate the Archimedes' force, we can use the formula:

Archimedes' force = weight of the fluid displaced

1. For a metal cylinder with a volume of 200 cm^3 fully immersed in water, we can calculate the Archimedes' force as follows:

The weight of the fluid displaced is equal to the weight of the water that is displaced by the cylinder. The weight of water displaced can be calculated using the density of water and the volume of the cylinder.

The density of water is approximately 1 g/cm^3 or 1000 kg/m^3.

Therefore, the weight of the water displaced is: \[ \text{Weight} = \text{Volume} \times \text{Density} \times \text{Acceleration due to gravity} \]

Substituting the given values: \[ \text{Weight} = 200 \, \text{cm}^3 \times 1 \, \text{g/cm}^3 \times 9.81 \, \text{m/s}^2 \]

Calculating the weight of the water displaced gives us the Archimedes' force for the fully immersed cylinder.

Archimedes' force for the fully immersed cylinder is approximately 1.962 N.

2. Now, let's calculate the Archimedes' force for a body with a volume of 2 m^3, with a quarter of its volume submerged in water.

The Archimedes' force for a body submerged in a fluid is equal to the weight of the fluid displaced.

Given that a quarter of the body's volume is submerged, the volume of water displaced is \( \frac{1}{4} \times 2 \, \text{m}^3 = 0.5 \, \text{m}^3 \).

Using the density of water (1000 kg/m^3) and the volume of water displaced, we can calculate the weight of the water displaced and hence the Archimedes' force.

Archimedes' force for the body with a quarter of its volume submerged in water is approximately 4905 N.

Conclusion

The Archimedes' force is a crucial concept in fluid mechanics and plays a significant role in determining the buoyancy of objects submerged in fluids. It is directly related to the weight of the fluid displaced by the object and is essential for understanding the behavior of objects in fluids.