Final answer:
The mass of the load lifted by the crane with a power consumption of 1020 kJ/s and an efficiency of 80% is approximately 17.076 metric tonnes, after calculating the useful work and taking into account the gravitational force over the height of 40 m.
Step-by-step explanation:
The mass of the load lifted by the crane can be determined by understanding the relationship between power, work, and energy. Given that the crane consumes electric power at a rate of 1020 kJ/s for 8.2 seconds, the total energy used can be found by multiplying power by time, resulting in 8376 kJ. Considering that the crane's efficiency is 80%, the useful energy is only 80% of the total energy consumed. Therefore, the useful work done (Wuseful) in lifting the load is:
Wuseful = 0.8 × 8376 kJ = 6700.8 kJ
The work done to lift the load against gravity equals the weight of the load (m × g, where m is the mass and g is the gravitational acceleration 9.81 m/s2) multiplied by the height (h).
Wuseful = m × g × h
By re-arranging the equation to solve for m and substituting the values:
m = ⅛ (Wuseful) / (g × h)
m = ⅛ (6700.8 × 103) / (9.81 × 40)
m = ⅛ (6700800 J) / (392.4 J/kg)
m = 17075.79 kg
Since 1 metric tonne equals 1000 kilograms, the mass of the load is 17.07579 metric tonnes.