The lift uses an internal combustion engine with an efficiency of 30%. With the help of an elevator

The lift uses an internal combustion engine with an efficiency of 30%. With the help of an elevator, sand weighing 150 tons was transferred from a pit 40 m deep to the surface of the earth. How many liters of gasoline did you use?

Efficiency = 30%.
mp = 150 t = 150,000 kg.
g = 10 N / kg.
h = 40 m.
q = 4.6 * 10 ^ 7 J / kg.
ρ = 710 kg / m3.
Vb -?
The efficiency coefficient shows what part of the spent work Az, expressed as a percentage, goes into useful work Ap: Efficiency = Ap * 100% / Az.
We express the useful work when lifting the body Ap by the formula: Ap = m * g * h, where m is the mass of sand, g is the acceleration of gravity, h is the height of the rise of sand.
The expended work Az is expressed by the formula: Az = q * mb, where q is the specific heat of combustion of gasoline, mb is the mass of gasoline that has burned.
mb = ρ * Vb.
Efficiency = m * g * h * 100% / q * ρ * Vb.
Vb = m * g * h * 100% / q * ρ * efficiency.
Vb = 150,000 kg * 10 N / kg * 40 m * 100% / 4.6 * 10 ^ 7 J / kg * 710 kg / m3 * 30% = 0.006 m3.
Answer: to raise the sand, it is necessary to burn Vb = 0.006 m3 = 6 liters of gasoline.



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