Complete question is;
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) 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:
A) Power of Niagara Falls = 1.176 × 10⁹ W
B) 78.4 × 10⁶ bulbs
Step-by-step explanation:
A) We are given;
The mass flow rate of Niagara falls = 2,400,000 kg/s
The average height of the fall = 50 meters
Gravitational potential energy = mass (kg) x height (m) x gravity (9.8 m/s²)
Now, formula for power is; workdone/time taken.
Thus it's potential energy/time taken.
Hence;
Power = (mass (kg) x height (m) x gravity (9.8 m/s²))/time(s)
We know that mass/time is mass flow rate.
Thus; power = mass flow rate (kg/s) × height (m) × gravity (9.8 m/s²)
Thus;
Power of Niagara Falls = 2400000 × 50 × 9.8 m/s²
Power of Niagara Falls = 1.176 × 10⁹ W
B) The number(n) of 15 W LED light bulbs Niagara falls could power is given by the relationship;
n × 15 W = 1.176 × 10⁹ W
Thus;
n = 1.176 × 10⁹ W/(15 W)
n = 78.4 × 10⁶ light bulbs
The number of 15 W LED light bulbs Niagara falls could power = 78.4 × 10⁶ bulbs