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 graviatational potential energy of falling water per second = mass (kg) x height (m) x gravity (9.8 m/s2), what is the power of Niagara Falls? How many 15 W LED light bulbs could it power?

Answer 1

1) The power of Niagara Falls is 1.176 × 10⁹ W

2) The number of 15 W LED light bulbs it could power is 78.4 × 10⁶ light bulbs

Step-by-step explanation:

1) The Niagara falls water mass flow rate = 2,400,000 kg/s

The height of the fall = 50 meters

The gravitational potential energy = Mass (kg) × height (m) × gravity (9.8 m/s²)

The power = The energy converted per second = Mass flow rate (kg/s) × height (m) × gravity (9.8 m/s²)

Therefore;

The power of Niagara Falls= 2,400,000 kg/s × 50 m ×9.8 m/s²= 1.176 × 10⁹ W

The power of Niagara Falls = 1.176 × 10⁹ W

2) The number, n, of 15 W LED light bulbs it could power is given by the relation;

n × 15 W = 1.176 × 10⁹ W

∴ n = 1.176 × 10⁹ W/(15 W) = 78.4 × 10⁶ light bulbs

The number of 15 W LED light bulbs it could power = 78.4 × 10⁶ light bulbs.