Question

Определить мощность электродвигателя с помощью которого поднимается груз массой 2000 кн на высоту 30 м за время 40 с если коэффициент полезного действия механизма равен 0,8

Answer 1

Работа вычисляется по формуле: A = FS, где A - работа, F - сила, S - путь.
Работа, которую нужно совершить двигателю, чтобы поднять груз A = 2 000 000Н * 30м = 60 000 000 Дж. Т.к. КПД двигателя равен 0,8, то работа по поднятию грауза - это 0,8, соответственно вся работа = 60 000 000Дж / 0,8 = 75 000 000Дж.
Мощность рассчитывается по формуле N = A / t = 75 000 000Дж / 40с = 1 875 000Вт = 1 875кВт = 1,875мВт

Answer 2

Calculation of Motor Power

To determine the power of the electric motor required to lift a load of 2000 kN to a height of 30 m in 40 s, we can use the formula:

Power = Work / Time

The work done in lifting the load can be calculated using the formula:

Work = Force x Distance

In this case, the force is the weight of the load, which is equal to its mass multiplied by the acceleration due to gravity. The distance is the height to which the load is lifted.

Given: - Mass of the load = 2000 kN - Height = 30 m - Time = 40 s - Efficiency of the mechanism = 0.8

First, let's convert the mass of the load from kilonewtons (kN) to kilograms (kg): - 1 kN = 1000 N - 1 N = 1 kg * m/s^2

Therefore, 2000 kN = 2000 * 1000 N = 2,000,000 N.

Now we can calculate the work done: Work = Force x Distance = (2,000,000 N) x (30 m)

Next, we can calculate the power: Power = Work / Time = (Work) / (40 s)

Finally, we need to take into account the efficiency of the mechanism. The actual power required by the motor will be higher than the calculated power due to losses in the system. The actual power can be calculated by dividing the calculated power by the efficiency: Actual Power = Power / Efficiency

Let's calculate the power and the actual power:

Work = (2,000,000 N) x (30 m) = 60,000,000 N*m

Power = (60,000,000 N*m) / (40 s)

Actual Power = Power / Efficiency = (Power) / (0.8)

Now we can calculate the values:

Work = 60,000,000 N*m

Power = (60,000,000 N*m) / (40 s)

Actual Power = (Power) / (0.8)

Using the given values and the formulas above, the power of the electric motor required to lift the load is approximately 1,500,000 watts or 1,500 kilowatts.

Please note that the above calculations assume ideal conditions and do not take into account factors such as friction, losses, or other inefficiencies in the system. The actual power required may vary depending on these factors.