Question

Подъемный кран приводится в действие мощностью 10кВт. Сколько времени нужно, чтобы поднять на высоту 50м. груз массой 2т, если КПД = 75%.

Answer 1

Дано:
Pз= 10 кВт = 10000 Вт
h = 50 м
m = 2 т = 2000 кг
ŋ = 0,75
g ≈ 10 м/с²
Найти: t - ?
Решение:
ŋ = P п/P з
ŋ = (mgh/t)/ Pз
t = mgh/Pз×ŋ
t = 2000 кг × 10 м/с² × 50 м/10000 Вт × 0,75 ≈ 133,3 с

Answer 2

Calculating Time Required to Lift a 2-ton Load to a Height of 50m Using a 10kW Power with 75% Efficiency

To calculate the time required to lift a 2-ton load to a height of 50m using a 10kW power with 75% efficiency, we can use the following formula:

Time = Work / Power

Where: - Time is the time required to lift the load to the given height. - Work is the work done, which is equal to the potential energy gained by the load. - Power is the power input to the system. - Efficiency is the efficiency of the system.

Calculating Work Done

The work done to lift the load to a height of 50m can be calculated using the formula:

Work = Force × Distance

In this case, the force required to lift the load is equal to its weight, and the distance is the height to which it is lifted.

Work = Force × Distance = Mass × Acceleration due to gravity × Height

Given: - Mass = 2 tons = 2000 kg - Acceleration due to gravity (g) = 9.81 m/s^2 - Height = 50m

Work = 2000 kg × 9.81 m/s^2 × 50m

Calculating Time

Now, we can use the formula mentioned earlier to calculate the time required to lift the load to the given height using a 10kW power with 75% efficiency.

Time = Work / (Power × Efficiency)

Substitute the values: - Work = Calculated above - Power = 10kW - Efficiency = 75%

Time = (2000 kg × 9.81 m/s^2 × 50m) / (10kW × 0.75)

Calculating the Result

Now, let's calculate the time required using the given values.

Time = (2000 kg × 9.81 m/s^2 × 50m) / (10kW × 0.75) Time ≈ 130.8 seconds

So, it would take approximately 130.8 seconds to lift the 2-ton load to a height of 50m using a 10kW power with 75% efficiency.