Question

Двигатель подъемного крана мощностью 6 кВт поднимает груз массой 6 т на высоту 8 м. Определите время подъема груза, если КПД установки равен 80%.( решите пожалуйста и объяснить решение) (полностью поясните решение пожалуйста).

Answer 1

полезная  работа   A = mgh = 6000*10*8 =480000 Дж

полная работа  An = A/кпд =480000 / 80% *100%=600000 Дж

 

время подъема  t = An/P =600000 Дж / 6000 Вт = 100 с = 1.67 мин

Answer 2

По формуле КПД=Ап / Aз. ( Ап- полезная работа ( Ап=m*g*h) , Аз-затраченная работа
( Аз=N*t ( N-мощность=6000Вт, t-время).Подставим и выразим t.
КПД=m*g*h / N*t ,
t=m*g*h / N*КПД. (КПД=0,8 , m=6000кг ( в системе СИ)).
t=6000*10*8 / 6000*0,8=100c.
t=100c

Answer 3

Calculation of Time for Lifting the Load

To calculate the time it takes for the crane to lift a load, we can use the formula:

Time = Work / Power

Where: - Work is the amount of work done, which is equal to the product of the force applied and the distance traveled. - Power is the rate at which work is done.

In this case, the work done is equal to the product of the force applied (mass of the load multiplied by the acceleration due to gravity) and the distance traveled (height of the lift). The power is given as 6 kW, but we need to take into account the efficiency of the system, which is 80%.

Let's calculate the time step by step:

1. Calculate the work done: - Force = mass * acceleration due to gravity - Force = 6 t * 9.8 m/s^2 (Note: 1 t = 1000 kg) - Force = 6000 kg * 9.8 m/s^2 - Force = 58800 N - Work = Force * distance - Work = 58800 N * 8 m - Work = 470400 J

2. Calculate the power taking into account the efficiency: - Power = 6 kW * 0.8 - Power = 4.8 kW

3. Calculate the time: - Time = Work / Power - Time = 470400 J / 4800 W (Note: 1 kW = 1000 W) - Time = 98 seconds

Therefore, it will take approximately 98 seconds for the crane to lift the 6-ton load to a height of 8 meters, assuming an efficiency of 80%.