Physics Q. Potential Energy

Question

Approximately 6.6 x 106 kg of water drops 53 m over

Niagara Falls every second. How much potential energy

is lost every second by the falling water?

I found the PE to be 3.43*10^9 J but I can't figure out this next one.

If the utility company sold this energy at an industrial rate of 11.7 cents per kW-hr, what would be their yearly income from this source? Give your answer in dollars.

Answer 1

You have calculated that the potential energy lost by the falling water every second is 3.43 x 10^9 J.

To determine the yearly income from selling this energy, we need to convert the energy from joules to kilowatt-hours, and then multiply by the industrial rate of 11.7 cents per kilowatt-hour.

1 kilowatt-hour (kWh) = 3,600,000 joules (J)

Converting the energy loss to kilowatt-hours:

Energy loss per second = 3.43 x 10^9 J

Energy loss per hour = 3.43 x 10^9 J/s × 3600 s/h = 1.2348 x 10^13 J/h

Energy loss per year = 1.2348 x 10^13 J/h × 8760 h/year = 1.079 x 10^17 J/year

Converting to kilowatt-hours:

Energy loss per year = 1.079 x 10^17 J/year ÷ 3,600,000 J/kWh = 2.9983 x 10^10 kWh/year

Multiplying by the industrial rate:

Income per year = 2.9983 x 10^10 kWh/year × $0.117/kWh = $3.51 x 10^9/year

Therefore, the utility company's yearly income from selling the potential energy lost by the falling water at Niagara Falls would be $3.51 billion.