Question

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 1

Explanation:

It is given that,

Water flows over Niagara Falls at the average rate of 2,400,000 kg/s

The average height of the falls is 50 m

We need to find the power of Niagara Falls.

The gravitational potential energy of falling water is given by :

P = mgh

Power is rate of doing work i.e.

$P=\dfrac{W}{t}\\\\P=\dfrac{mgh}{t}\\\\P=\dfrac{m}{t}\times gh$

We have, m/t =  2,400,000 kg/s

So,

$P=2400000\times 9.8\times 50\\\\P=1.176\times 10^9\ W$

If the number of bulbs are n that could power 15 W LED, the,

$n=\dfrac{1.176\times 10^9}{15}\\\\n=78400000\ \text{bulbs}$