The crane is powered by a 15 kW motor. Find the efficiency of the engine

The crane is powered by a 15 kW motor. Find the efficiency of the engine if it lifts a load weighing 3 tons to a height of 30 m in 1 min 40 s.

Ns = 15 kW = 15000 W.

t = 1 min 30 s = 90 s.

h = 30 m.

m = 3 t = 3000 kg.

g = 10 m / s2.

Efficiency -?

According to the definition, the efficiency coefficient of the crane efficiency shows what part of the expended work Az, expressed as a percentage, goes into the useful Ap.

The useful work of Ap is that a body of mass m was lifted to a height h: Ap = m * g * h, where g is the acceleration of gravity.

The expended work is the work Az, which is performed by the crane engine: Az = Nc * t, where Nc is the consumed power of the crane motor, t is the engine running time.

Efficiency = m * g * h * 100% / Nc * t.

Efficiency = 3000 kg * 10 m / s2 * 30 m * 100% / 15000 W * 90 s = 67%.

Answer: the crane has an efficiency of 67%.