With the help of a rope, a concrete cube with a volume of 0.5 m³ is evenly and slowly lifted

With the help of a rope, a concrete cube with a volume of 0.5 m³ is evenly and slowly lifted from the bottom of a lake 10 m deep. What kind of mechanical work is being done?

To find out the mechanical work performed when lifting a given concrete cube, we use the formula: Amech = F * S = (Fт – FA) * h = (m * g – ρо * g * Vк) * h = (ρb * Vк * g – ρо * g * Vк) * h = (ρb – ρо) * h * Vк * g.

Const: ρb is the density of lightweight concrete (ρb = 1800 … 2200 kg / m3; we take ρb = 2000 kg / m3); ρо is the density of lake water (ρо = 103 kg / m3); g – acceleration due to gravity (g ≈ 9.81 m / s2).

Data: h – depth of the lake, path of the concrete cube (h = 10 m); Vк – the volume of the concrete cube (Vк = 0.5 m3).

Let’s perform the calculation: Amech = (ρb – ρo) * h * Vk * g = (2000 – 1000) * 10 * 0.5 * 9.81 = 49.05 * 103 J.

Answer: When lifting a given concrete cube, work is done at 49.05 kJ.