Concrete slab with a volume of 2m3 submerged in water. What force must be applied to keep it in the water? in the air?

To calculate the value of the required force to hold the specified concrete slab in water and air, we use the formula: Fр = Fт – Fa = m * g – ρх * g * V = ρb * V * g – ρх * g * V = (ρb – ρх) * V * g.

Data: ρb is the density of the concrete slab (for heavy concrete ρb = 2000 … 2500 kg / m3; let us take ρb = 2250 kg / m3); ρwater – water density (ρwater = 1000 kg / m3); ρair – air density (let’s take ρair = 1.204; t = 20 ºС); V is the volume of the slab (V = 2 m3); g – acceleration due to gravity (g ≈ 10 m / s2).

Calculation: 1) Fр = (ρb – ρwater) * V * g = (2250 – 1000) * 2 * 10 = 25 * 10 ^ 3 H = 25 kN;

2) Fр = (ρb – ρair) * V * g = (2250 – 1.204) * 2 * 10 = 44975.92 N ≈ 45 kN.

Answer: To hold the specified concrete slab in water, a force of 25 kN is required; in the air – 45 kN.