Question

Определить силу, действующую на поршень площадью 100 см 2, если на поршень площадью 250 cм2 приложена сила 200 Н.Одно и тоже тело погружают по очереди в воду, нефть. Во сколько раз отличается сила Архимедова при этом?Найти гидростатическое давление воды высотой 5 м.​

Answer 1

Решение:

1)

S₁ = 100 см²

S₂ = 250 см²

F₂ = 200 H

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$F_1 = F_2\cdot \dfrac{S_1}{S_2} =200\cdot \dfrac{100}{250} = 80~(N).$

$\boxed{F_1 = 80 ~H}$

2)

ρ₁ = 1000 кг/м³ - плотность воды

ρ₂ = 800 кг/м³ - плотность нефти

Архимедова сила

Fa = ρ · V · g

Отношение сил Архимеда

$\dfrac{F_{a1}}{F_{a2}} = \dfrac{\rho_1}{\rho_2}$

$\dfrac{F_{a1}}{F_{a2}} = \dfrac{1000}{800}=1,25.$

$\boxed {\dfrac{F_{a1}}{F_{a2}} = 1,25}$

3)

ρ = 1000 кг/м³ - плотность воды

g = 10 Н/кг

h = 5 м

Гидростатическое давление

p = ρ · g · h = 1000 · 10 · 5 = 50 000 (Па) = 50 кПа

$\boxed {p = 50~kPa}$

Answer 2

Calculating Force on the Piston:

To determine the force acting on the piston with an area of 100 cm^2 when a force of 200 N is applied to the piston with an area of 250 cm^2, we can use the formula:

Force = Pressure × Area

First, we can calculate the pressure applied to the larger piston using the given force and area:

Pressure = Force / Area

Then, we can use the calculated pressure to find the force acting on the smaller piston:

Force = Pressure × Area

Let's calculate the force on the smaller piston:

Step 1: Calculate the pressure on the larger piston: The pressure applied to the larger piston can be calculated using the given force and area: Pressure = 200 N / 250 cm^2

Step 2: Calculate the force on the smaller piston: Using the calculated pressure, we can find the force acting on the smaller piston: Force = Pressure × 100 cm^2

Archimedes' Force in Different Substances:

When the same object is submerged in water and then in oil, the difference in the Archimedes' force can be determined by comparing the densities of water and oil. The Archimedes' force is given by the formula:

Archimedes' Force = Density of Fluid × Volume of Displaced Fluid × Acceleration due to Gravity

The ratio of the Archimedes' force in water to the Archimedes' force in oil can be found by comparing the densities of the two substances.

Calculating Hydrostatic Pressure of Water:

The hydrostatic pressure of water at a given depth can be calculated using the formula:

Hydrostatic Pressure = Density of Fluid × Acceleration due to Gravity × Depth

Given that the height of the water column is 5 m, we can calculate the hydrostatic pressure of water at this depth using the density of water and the acceleration due to gravity.

Let's calculate the force on the smaller piston, the difference in Archimedes' force in water and oil, and the hydrostatic pressure of water at a depth of 5 m.