Question

Подъемный кран поднимает равномерно груз массой 500 кг на высоту 10 м за 50 с. Определите КПД кран , если мощность его двигателя 1,5 кВт

Answer 1

КПД = (работа полезная/работа затраченная) * 100 %
КПД = 500*10*10/1500*50 = 0,67 *100 % = 67 %
Ответ: КПД крана = 67 %

Answer 2

Calculation of Efficiency (КПД) of the Crane

To calculate the efficiency (КПД) of the crane, we need to use the formula:

КПД = (Useful Output Power / Input Power) x 100%

In this case, the useful output power is the power required to lift the load, and the input power is the power of the crane's engine.

Given: - Mass of the load (m) = 500 kg - Height (H) = 10 m - Time taken (t) = 50 s - Power of the engine (P) = 1.5 kW

To find the useful output power, we can use the formula:

Useful Output Power = Work Done / Time

The work done to lift the load can be calculated using the formula:

Work Done = Force x Distance

The force required to lift the load can be calculated using the formula:

Force = Mass x Acceleration due to gravity

Acceleration due to gravity (g) is approximately 9.8 m/s^2.

Let's calculate the efficiency (КПД) of the crane step by step:

1. Calculate the force required to lift the load: - Force = Mass x Acceleration due to gravity - Force = 500 kg x 9.8 m/s^2 - Force = 4900 N

2. Calculate the work done to lift the load: - Work Done = Force x Distance - Work Done = 4900 N x 10 m - Work Done = 49000 Nm (or Joules)

3. Calculate the useful output power: - Useful Output Power = Work Done / Time - Useful Output Power = 49000 Nm / 50 s - Useful Output Power = 980 W (or 0.98 kW)

4. Calculate the efficiency (КПД): - Efficiency (КПД) = (Useful Output Power / Input Power) x 100% - Efficiency (КПД) = (0.98 kW / 1.5 kW) x 100% - Efficiency (КПД) = 65.33%

Therefore, the efficiency (КПД) of the crane is approximately 65.33%.

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