Determine the power of the crane motor, evenly lifting a load weighing 3 tons to a height of 10

Determine the power of the crane motor, evenly lifting a load weighing 3 tons to a height of 10 meters in 50 seconds with an efficiency of 75%.

These tasks: m (mass of uniformly lifted load) = 3 t (in SI m = 3 * 10 ^ 3 kg); h (lifting height) = 10 m; t (duration of the crane operation) = 50 s; η (crane efficiency) = 75% (0.75).

Reference values: g (acceleration due to gravity) ≈ 10 m / s2.

We express the engine power of the crane under consideration from the formula: η = Np / Nd = A / (Nd * t) = m * g * h / (Nd * t), whence Nd = m * g * h / (η * t).

Let’s make a calculation: Nd = 3 * 10 ^ 3 * 10 * 10 / (0.75 * 50) = 8 * 10 ^ 3 W (8 kW).