A walking excavator throws out 14m3 of soil at a time, lifting it to a height of 20m

A walking excavator throws out 14m3 of soil at a time, lifting it to a height of 20m, the weight of a bucket without soil is 20kN. Determine the work done to lift the soil and bucket.

V = 14 m3.

h = 20 m.

g = 9.8 m / s2.

Pk = 20 kN = 20,000 N.

ρ = 1500 kg / m3.

A -?

The work of a walking excavator will be determined by the formula: A = F * S, where F is the force of the engine that lifts the bucket, S is the movement of the bucket.

S = h.

We will assume that the bucket with the soil is raised evenly, then the force of the excavator F is equal to the weight of the bucket with the soil P: F = P.

The weight of the bucket with soil P will be the sum of the weight of the bucket Pk and the weight of the soil Pg: P = Pk + Pg.

The weight of the soil Рg is expressed by the formula: Рg = mg * g, where mg is the mass of the soil, g is the acceleration of gravity.

mg = V * ρ.

Pr = V * ρ * g.

A = (Pк + V * ρ * g) * h.

A = (20,000 N + 14 m3 * 1,500 kg / m3 * 9.8 m / s2) * 20 m = 4,516,000 J.

Answer: when lifting the bucket with the ground, work is performed A = 4516000 J.