The crane motor in 100 s evenly lifts a load weighing 5 tons to a height of 5 m

The crane motor in 100 s evenly lifts a load weighing 5 tons to a height of 5 m. The efficiency of the crane is 0.8. What power should the crane motor develop?

t = 100 s.

m = 5 t = 5000 kg.

g = 10 m / s2.

h = 5 m.

Efficiency = 0.8.

Nz -?

The efficiency of the crane shows how much of the spent mechanical work Az, when lifting the load, goes into useful work Ap.

Efficiency = Ap / Az.

The useful work of the crane Ap is expressed by the formula: Ap = m * g * h, where m is the mass of the lifted load, h is the lifting height of the load, g is the acceleration of gravity.

The expended work Az will be expressed by the formula: Az = Nz * t, where Nz is the power that the crane motor develops, t is the time of lifting the load.

Efficiency = m * g * h / Nz * t.

Nz = m * g * h / efficiency * t.

Nz = 5000 kg * 10 m / s2 * 5 m / 0.8 * 100 s = 3125 W.

Answer: when lifting a load, the crane engine develops a power of Ns = 3125 W.