What power should the motor of a lift that drops boxes with salt to a height of 14 m

What power should the motor of a lift that drops boxes with salt to a height of 14 m, if the weight of each box is 30 kg, and the feed rate is 8 boxes per minute.

When lifting a load of mass m to a certain height h, work A is performed against gravity, equal to the change in potential energy: A = m ∙ g ∙ h – m ∙ g ∙ h₀ where h₀ and h are the initial and final height of the body above the earth’s surface, the coefficient g ≈ 9.8 N / kg. Since h₀ = 0 m, then А = m ∙ g ∙ h. The power N of the engine is found as the work done per unit of time: N = A / t. Then: N = m ∙ g ∙ h / t. From the condition of the problem it is known that the boxes with salt are fed by a hoist to a height of h = 14 m, the mass of each box is m₀ = 30 kg, and the feed rate is 8 boxes per minute, that is, the number of boxes n = 8, time t = 1 min = 60 c then the load being lifted has a mass m₀ = n ∙ m₀, which means:

A = n ∙ m₀ ∙ g ∙ h.

Let us substitute the values ​​of the quantities into the calculation formula and find how much power the motor of the elevator supplying the boxes with salt should have:

N = (8 ∙ 30 kg ∙ g ∙ 14 m) / 60 s; N = 56 W.

Answer: engine power 56 W.