Question

Башенный кран равномерно поднимает груз массой 380кг на высоту 22м за 100с. Определите ток в электродвигателе при напряжении 220В , если известно, что КПД электродвигателя крана равен 38%.

Answer 1

Решение внизу на фотографии.

Answer 2

Calculation of Current in the Electric Motor

To determine the current in the electric motor of the tower crane, we can use the power equation:

Power (P) = Voltage (V) × Current (I)

We are given the voltage (V) as 220V and the efficiency (η) of the electric motor as 38%. We need to find the current (I).

First, let's calculate the power (P) using the formula:

Power (P) = Work Done / Time

The work done can be calculated using the formula:

Work Done = Force × Distance

In this case, the force is the weight of the load being lifted, which is 380 kg, and the distance is the height to which the load is lifted, which is 22 m.

Substituting the values into the formula, we get:

Work Done = 380 kg × 9.8 m/s^2 × 22 m

Now, we can calculate the power:

Power (P) = Work Done / Time = (380 kg × 9.8 m/s^2 × 22 m) / 100 s

Next, we can calculate the input power to the electric motor using the efficiency formula:

Efficiency (η) = Output Power / Input Power

Since the efficiency is given as 38%, we can rewrite the formula as:

0.38 = Output Power / Input Power

Rearranging the formula, we get:

Input Power = Output Power / 0.38

Now, we can substitute the value of the power we calculated earlier into the formula to find the input power:

Input Power = (380 kg × 9.8 m/s^2 × 22 m) / 100 s / 0.38

Finally, we can calculate the current (I) using the power equation:

Power (P) = Voltage (V) × Current (I)

Rearranging the formula, we get:

Current (I) = Power (P) / Voltage (V)

Substituting the values, we get:

Current (I) = Input Power / Voltage (V)

Now, we can substitute the values of the input power and voltage into the formula to find the current:

Current (I) = [(380 kg × 9.8 m/s^2 × 22 m) / 100 s / 0.38] / 220 V

Calculating this expression will give us the current in the electric motor of the tower crane.

Please note that the above calculations assume ideal conditions and do not take into account any losses or inefficiencies in the system.