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

Power,
`P=1.176* 10^9\ W`

No of bulbs = 78400000

Step-by-step 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,

`P=(W)/(t)\\\\P=(mgh)/(t)\\\\P=(m)/(t)* gh`

So,

`P=2400000* 9.8* 50\\\\P=1.176* 10^9\ W`

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

`n=(1.176* 10^9)/(15)\\\\n=78400000\ \text{bulbs}`

It means that the number of bulbs are 78400000.