# The crane lifts a load weighing 3 tons to a height of 30 m in one minute determine the net power of the crane

t = 1 min = 60 s ..

m = 3 t = 3000 kg.

g = 10 m / s2.

h = 30 m.

Nп -?

The useful power of the crane Np is called a scalar physical quantity that shows the speed of performing useful mechanical work Ap. The useful power of the crane Np is expressed by the formula: Np = Ap / t, where t is the time of performing useful mechanical work.

If we assume that the lifting of the load is uniformly rectilinear, then the useful mechanical work Ap performed by it will be determined by the formula: Ap = m * g * h, where m is the mass of the lifted load, g is the acceleration of gravity, h is the height of the lifting of the load.

The useful power of the crane Nп will be determined by the formula: Nп = m * g * h / t.

Np = 3000 kg * 10 m / s2 * 30 m / 60 s = 15000 W = 15 kW.

Answer: the useful power of the crane is Np = 15 kW.