Question

подьемный кран должен в течении 8 ч рабочего дня поднять 3000т строительных материалов на высоту 9м. Какова мощность двигателя крана, если к.п.д установки 60%

Answer 1

Работа по перемещению груза на высоту

 

$A= mgh = 3 \cdot 10^6 \cdot 9.8 \cdot 9 = 2,65 \cdot 10^8$ Дж

 

С учетом к.п.д. энергия, затрачиваемая двигателем

 

$E=\frac{A}{0,6}=4,42 \cdot 10^8$ Дж

 

Если считать, что подъемный кран тратит половину времени на подъем груза, то мощность двигателя

 

$P=\frac{E}{t}=\frac{4,42 \cdot 10^8}{4 \cdot 3600}\approx3,07 \cdot 10^4$ Ватт

 

Ответ: мощность двигателя 30,7 кВт 

Answer 2

Calculation of Power Required for the Crane

To calculate the power required for the crane to lift 3000 tons of construction materials to a height of 9 meters within 8 hours, we can use the formula:

Power (P) = Work done (W) / Time (t)

The work done can be calculated as the product of the force (F) and the distance (d) lifted:

Work done (W) = Force (F) x Distance (d)

Given that the force is equal to the weight of the materials lifted, and the weight is equal to the mass (m) multiplied by the acceleration due to gravity (g), we can rewrite the formula as:

Work done (W) = m x g x d

Substituting the given values, we have:

Work done (W) = 3000 tons x 9.8 m/s^2 x 9 meters

Now, we can calculate the power:

Power (P) = (3000 tons x 9.8 m/s^2 x 9 meters) / (8 hours)

Before calculating the power, we need to convert the units to a consistent system. Let's convert the weight from tons to kilograms and the time from hours to seconds:

Power (P) = (3000 tons x 1000 kg/ton x 9.8 m/s^2 x 9 meters) / (8 hours x 3600 seconds/hour)

Simplifying the equation:

Power (P) = (3000 x 1000 x 9.8 x 9) / (8 x 3600)

Now, let's calculate the power:

Power (P) = 73500 watts

Therefore, the power required for the crane to lift 3000 tons of construction materials to a height of 9 meters within 8 hours is 73500 watts.