Using a hoist from the bottom of a lake with a depth of 20 m, a slab weighing 2 tons and a volume of 0.8 m³ was raised in 2 minutes to determine the power of the hoist, the density of water is equal to 1000 kg / m³.
m = 2 t = 2000 kg.
g = 9.8 m / s2.
h = 20 m.
V = 0.8 m3.
t = 2 min = 120 s.
ρ = 1000 kg / m3.
∠α = 0 °.
Power N is determined by the formula: N = A / t, where A – work, t – time of work.
Work A is determined by the formula: A = F * S * cosα, where F is the force that lifts the body, S is the movement of the body, ∠α is the angle between F and S.
S = h, ∠α = 0 °, cos0 ° = 1.
Since the slab is raised in water, then F = m * g – ρ * g * V = g * (m – ρ * V).
N = g * h * (m – ρ * V) / t.
N = 9.8 m / s2 * 20 m * (2000 kg – 1000 kg / m3 * 0.8 m3) / 120 s = 1960 W.
Answer: the power of the hoist is N = 1960 W.
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