Question

Подъёмный кран равноускоренно поднимает груз массой 1140 кг из состояния покоя на высоту 10 м. Электродвигатель крана питается от сети напряжением 380 В и в конце подъёма имеет КПД, равный 60%. Сила тока в обмотке электродвигателя 102 А. Определите время подъёма груза.

Answer 1

m=1140 кг

h=10 м

U=380 В

кпд ή=60%=0.6

I=102A

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t -?

 

РЕШЕНИЕ

 

полная энергия электродвигателя  E=UIt

полезная работа по подъему A= mgh

ή = A/E =mgh / UIt 

t = mgh / (UIή ) =1140*10*10 /(380*102*0.6) = 4.9 c =5 c

ответ  4.9 c =5 c

Answer 2

Calculation of the Time Taken to Lift the Load

To calculate the time taken to lift the load, we can use the equation for work done:

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

In this case, the force is equal to the weight of the load, and the distance is the height it is lifted. The work done is equal to the change in potential energy of the load.

The formula for potential energy is:

Potential Energy (PE) = Mass (m) x Gravity (g) x Height (h)

Since the crane lifts the load with constant acceleration, we can use the equation for uniformly accelerated motion:

h = (1/2) x a x t^2

where: - h is the height (10 m), - a is the acceleration (which is equal to g, the acceleration due to gravity), - t is the time taken to lift the load.

By substituting the value of h into the equation, we get:

10 = (1/2) x g x t^2

Simplifying the equation, we have:

t^2 = (20 / g)

Taking the square root of both sides, we get:

t = sqrt(20 / g)

To find the value of g, we can use the standard acceleration due to gravity, which is approximately 9.8 m/s^2.

Now, let's calculate the time taken to lift the load.

Calculation:

Given: - Mass of the load (m) = 1140 kg - Height (h) = 10 m - Efficiency (η) = 60% = 0.6 - Current in the motor winding (I) = 102 A - Voltage (V) = 380 V

First, let's calculate the force (F) exerted by the load:

Force (F) = Mass (m) x Gravity (g)

Using the standard acceleration due to gravity (g = 9.8 m/s^2), we have:

F = 1140 kg x 9.8 m/s^2

Now, let's calculate the power (P) consumed by the motor:

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

Power (P) = 380 V x 102 A

Next, let's calculate the power output (P_out) of the motor:

Power Output (P_out) = Efficiency (η) x Power (P)

Power Output (P_out) = 0.6 x (380 V x 102 A)

Now, let's calculate the time taken to lift the load:

t = sqrt(2h / g)

t = sqrt(2 x 10 m / 9.8 m/s^2)

Finally, let's substitute the values and calculate the time taken to lift the load.

Calculation:

Force (F) = 1140 kg x 9.8 m/s^2

Power (P) = 380 V x 102 A

Power Output (P_out) = 0.6 x (380 V x 102 A)

t = sqrt(2 x 10 m / 9.8 m/s^2)

Please note that the calculations provided above are based on the given information and assumptions.