The power of the crane motor is 4.5 kW. How much weight can be lifted with this crane

The power of the crane motor is 4.5 kW. How much weight can be lifted with this crane to a height of 12 m in 0.5 minutes. The engine efficiency is 80%.

These tasks: Ns (crane motor power, consumed power) = 4.5 kW (4.5 * 103 W); h (height to which the load must be lifted) = 12 m; t (duration of the crane operation) = 0.5 min (30 s); η (motor efficiency) = 80%.

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

We express the maximum cargo mass from the formula: η = Np / Nz = (A / t) / Nz = ΔEp / (t * Nz) = m * g * h / (t * Nz), whence m = η * t * Nz / (g * h).

Calculation: m = 0.8 * 30 * 4.5 * 103 / (10 * 12) = 900 kg.