Final answer:
To calculate the time for a crane to lift a 2100 kg beam to 120 m with a power of 6900 W, we determine the work done and then use the power-time relationship. It will approximately take the crane 356 seconds to complete the lift.
Step-by-step explanation:
The subject of the question is related to the work done by a crane, which falls under the area of physics dealing with energy and power. Given the power of the crane's engine, the mass of the beam, and the height to which it needs to be lifted, the goal is to determine the time required to complete this task.
The time can be calculated using the formula for power, which is the rate at which work is done (Power = Work/Time). Work done by the crane can be found by using the work-energy principle (Work = Force × Distance), where the force is derived from the weight of the beam (Force = mass × gravitational acceleration).
To find the time required for the crane to lift a 2100 kg beam to a height of 120 m using 6900 W of power, we first must calculate the work done by the crane:
Work = Force × Distance
Force = mass × gravitational acceleration = 2100 kg × 9.8 m/s2
Work = (2100 kg × 9.8 m/s2) × 120 m = 2,457,600 J
Next, we use the power formula to find the time.
Time = Work/Power
Time = 2,457,600 J / 6900 W = 356 s
Therefore, it will take the crane approximately 356 seconds to lift the 2100 kg beam to a height of 120 m.