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.