Physics 2009 JAMB Past Questions - Question 10: if a cage containing a truck of coal weighing 750kg is raised to a height of 90m in 1minutes, what is the total power expended?

Correct Answer

C

Explanation

To find the total power expended to raise the cage with a truck of coal to a height of 90 meters in 1 minute, you can use the formula for power:

Power (P) = Work (W) / Time (t)

First, calculate the work done. The work done is equal to the change in potential energy of the cage-truck system as it is raised to a height of 90 meters. The formula for potential energy (PE) is:

PE = m * g * h

Where:
- m is the mass of the truck (750 kg)
- g is the acceleration due to gravity (approximately 9.81 m/s²)
- h is the height (90 m)

PE = 750 kg * 9.81 m/s² * 90 m = 661,087.5 joules

Now, you need to find the power, which is work done (W) divided by time (t). Since the time is given in 1 minute, you'll need to convert it to seconds since power is usually expressed in watts, and 1 watt is equal to 1 joule per second.

1 minute = 60 seconds

Power (P) = 661,087.5 joules / 60 seconds ≈ 11,018.13 watts (or 11.02 kilowatts)

So, the total power expended to raise the cage with the truck of coal to a height of 90 meters in 1 minute is approximately 11.02 kilowatts.