Question

Объем ящика 0,5 м³, вес его вместе с грузом 4 кН. Всплывет он или утонет в воде? (Найдите архимедову силу)

Answer 1

Fарх=roVg (ro - плотность воды) = 1000*0,5*10=5000
Масса груза 400 кг m=P/g

Answer 2

Calculating Archimedes' Force

To determine whether the box will float or sink in water, we can calculate the Archimedes' force acting on it. Archimedes' principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces.

The formula to calculate the Archimedes' force is:

Archimedes' Force (F_arch) = Density of Fluid (ρ) * Volume of Displaced Fluid (V) * Acceleration due to Gravity (g)

Applying the Formula

Given: - Volume of the box (V) = 0.5 m³ - Weight of the box and cargo (W) = 4 kN - Density of water (ρ) = 1000 kg/m³ (standard value) - Acceleration due to gravity (g) = 9.8 m/s²

We can calculate the Archimedes' force using the formula:

F_arch = ρ * V * g

Substituting the given values: F_arch = 1000 kg/m³ * 0.5 m³ * 9.8 m/s²

Calculating Archimedes' Force

Let's calculate the Archimedes' force using the given values:

F_arch = 1000 kg/m³ * 0.5 m³ * 9.8 m/s² = 4900 N

Conclusion

The Archimedes' force acting on the box is 4900 N. Since the weight of the box and cargo is 4000 N (4 kN), and the Archimedes' force is greater than the weight, the box will float in water.