If a cage containing a truck of coal weighing 750 kg is raised to a height of 90 m in a minute, what is the total power expended? [g = 10 ms2]
Answer Details
To solve this problem, we need to use the formula for power, which is:
Power = work/time
We first need to calculate the work done to lift the cage of coal. Work is given by the formula:
Work = force x distance
The force here is the weight of the cage of coal, which is given as 750 kg. We need to convert this to Newtons, which is the unit of force in the SI system:
Force = mass x gravity
Force = 750 x 10 = 7500 N
The distance lifted is 90 m. Hence, the work done is:
Work = force x distance = 7500 x 90 = 675000 J
The time taken to lift the cage is given as 1 minute, which is equal to 60 seconds. Hence, the power expended is:
Power = work/time = 675000/60 = 11250 W
Converting this to kilowatts, we get:
Power = 11250/1000 = 11.25 kW
Therefore, the answer is option C: 11.25 kW.