The walking excavator throws out 14m3 of soil at a time, lifting it to a height of 20m. Bucket weight without soil is 2 tons. Determine the work that the excavator engine performs during a single lift of the soil and bucket. Soil density 1500 kg / m3
V = 14 m3.
h = 20 m.
g = 9.8 m / s2.
mk = 2 t = 2000 kg.
ρ = 1500 kg / m3.
The work of force A is determined by the formula: A = F * S, where F is the force under which the body moves, S is the movement of the body under the action of the force F.
If we consider the lifting of the bucket with the soil to be uniform rectilinear, then the movement of the bucket with the soil S will be equal to the lifting height h, and the lifting force of the excavator F will be equal to the gravity of the bucket with the soil (mk + m) * g.
S = h, F = (mk + m) * g.
We find the mass of soil m in the bucket by the formula: m = V * ρ.
A = (mk + V * ρ) * g * h.
A = (2000 kg + 14 m3 * 1500 kg / m3) * 9.8 m / s2 * 20 m = 4508000 J.
Answer: the excavator engine does work A = 4,508,000 J.
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