. Шагающий экскаватор за один прием выбрасывает 14 м3 грунта, поднимая его при этом на высоту 20 м. Масса ковша без грунта равна 2 т. Плотность грунта 1500 кг/м3 . Какую работу совершает экскаватор по подъему ковша и грунта?
The excavator performs two different types of work in this situation: lifting the bucket and lifting the soil. To determine the total work, we need to calculate both separately and add them together.
First, let's calculate the work done in lifting the bucket. The work formula is given by W = mgh, where m is the mass of the object (in kilograms), g is the gravitational acceleration (9.8 meters per second squared), and h is the distance moved (in meters).
In this case, the mass of the bucket is 2000 kilograms and the distance lifted is 20 meters. We can plug these values into the formula and get:
Wbucket = (2000 kg)(9.8 m/s2)(20 m) = 392,000 Joules
Now, let's calculate the work done in lifting the soil. The volume of soil lifted in one go is 14 cubic meters (m3), and its density is 1500 kg/m3. Therefore, the mass of the soil lifted is (14 m3)(1500 kg/m3) = 21,000 kg.
With this information, we can use the same formula to calculate the work done in lifting the soil:
Wsoil = (21,000 kg)(9.8 m/s2)(20 m) = 4,116,000 Joules
Finally, we can calculate the total work done by the excavator by adding the two values together:
Wtotal = Wbucket + Wsoil = 392,000 J + 4,116,000 J = 4,508,000 Joules
