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Water flows over Niagara Falls at the average rate of 2,400,000 kg/s, and the average height of the falls is about 50 m. Knowing that the gravitational potential energy of falling water per second = mass (kg) × height (m) × gravity (9.8 m/s2), what is the power of Niagara Falls? How many 15 W LED light bulbs could it power?

Answer :

Answer:

Power, [tex]P=1.176\times 10^9\ W[/tex]

No of bulbs = 78400000

Explanation:

We have,

Water flows over Niagara Falls at the average rate of 2,400,000 kg/s, it mean it is mass per unit time i.e. m/t.

It falls from a height of 50 m

The gravitational potential energy of falling water is given by :

P = mgh

Power is equal to the work done divided by time taken. So,

[tex]P=\dfrac{W}{t}\\\\P=\dfrac{mgh}{t}\\\\P=\dfrac{m}{t}\times gh[/tex]

So,

[tex]P=2400000\times 9.8\times 50\\\\P=1.176\times 10^9\ W[/tex]

Let there are n bulbs that could power 15 W LED. It can be calculated by dividing the power by 15. So,

[tex]n=\dfrac{1.176\times 10^9}{15}\\\\n=78400000\ \text{bulbs}[/tex]

It means that the number of bulbs are 78400000.

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