Finding the yearly income from energy in W

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SUMMARY

The discussion focuses on calculating the yearly income generated from the potential energy of falling water at Niagara Falls, specifically using the conversion of potential energy to electrical energy. The correct calculation involves converting the power output of 1*10^9 W to kilowatts, resulting in 1*10^6 kW. The yearly energy output is determined by multiplying the hourly output by the total hours in a year (8760), followed by applying the industrial rate of 0.8 cents per kWh. The final income calculation yields a total of $2.52*10^11, confirming the importance of accurate unit conversions and understanding energy pricing.

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  • Understanding of electrical power units (W, kW, kWh)
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  • Familiarity with unit conversion and dimensional analysis
  • Awareness of pricing models for electrical energy
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Homework Statement



Approximately 1.7*10^6 kg of water drops 60 m over Niagara Falls every second. 1*10^9 J of potential energy is lost every second by the falling water. If an electrical generating plant could convert all of the potential energy into electrical energy it would have a power output of 1*10^9 W. If the utility company sold this energy at an industrial rate of 0.8 cents per kW-hour, what would their yearly income be from this source (give your energy in dollars)?

Homework Equations



1 kW =1000 W
365 days=1 year
8760 hours = 1 year

The Attempt at a Solution



1*10^9 W -> 1*10^6 kW

1*10^6 kW * 60 sec/min * 60 min/hour = 3.6 *10^9

3.6 *10^9 * 0.008 = 2.88*10^7

2.88*10^7 * 8760 = 2.52*10^11

it says this is wrong. I have one shot left. what am I doing wrong?


 
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This bit is wrong..

1*10^6 kW * 60 sec/min * 60 min/hour = 3.6 *10^9

If the output is 1*10^6 kW then after one hour it has delivered 1*10^6 kWH. You only need to multiply that by the number of hours there are in a year and the price per kWH.
 

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