Approximately 5.7 multiplied by 106 kg of water fall 50 m over Niagara Falls eac

Question

Approximately 5.7 multiplied by 106 kg of water fall 50 m over Niagara Falls each second.

(a) What is the decrease in the gravitational potential energy of the water-Earth system each second?
___J
(b) If all this energy could be converted to electrical energy by an electric generating plant (it cannot be), at what rate would electrical energy by supplied? (The mass of 1 m3 of water is 1000 kg.)
___W
(c) If the electrical energy were sold at 2 cents/kW·h, what would be the yearly cost?
___million dollars

Explanation / Answer

a) The decrease in potential energy due to fall of water is(this is amount of decrease per second)

          U = m g h

               = (5.7x10^6)(9.8)(50m)

               = 2.793x10^9 J

b) Power is energy per second. we got energy / s in part a

       P = 2.793x10^9 J

c) for one year, the time is 24 hrs x 365 days .so

     (2.793x10^9 W )( 24hrs x 365 days)(1kilowatt / 1000watt) (2cents / kwh)

   = 4.89x10^10 cents

converting into dollars

   = [(4.89x10^10 cents) $ /100 cents ](1 M$ / 10^6 $ )= 4.89x10^2 M$

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