Question

Подъёмный кран развивает мощность 10 кВт, равномерно поднимая груз массой 2 т. На какую высоту кран переместит груз за 30 с?

Answer 1

Calculation of the Height the Crane will Lift the Load

To calculate the height the crane will lift the load, we need to use the formula 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 the load is lifted.

Given: - Power of the crane: 10 kW - Mass of the load: 2 tons (2000 kg) - Time taken to lift the load: 30 seconds

To find the height the crane will lift the load, we need to calculate the work done by the crane. Since power is the rate at which work is done, we can use the formula:

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

Rearranging the formula, we get:

Work (W) = Power (P) x Time (t)

Substituting the given values:

Work (W) = 10 kW x 30 s = 300 kJ

Now, we can use the formula for work done to find the height:

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

Rearranging the formula, we get:

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

Substituting the given values:

Distance (d) = 300 kJ / 2000 kg x 9.8 m/s^2

Calculating the distance:

Distance (d) = 15.3 m

Therefore, the crane will lift the load to a height of 15.3 meters in 30 seconds.