Water flows over a section of Niagara Falls at
a rate of 2.1 × 106
kg/s and falls 59 m.
What is the power wasted by the waterfall?
The acceleration due to gravity is 9.8 m/s
2
.
Answer in units of W
power=energy per second = m g h / t = mass per second * g * h
= 2.1 * 10^6 * 9.81 * 59 = 1215 * 10^6 = 1.215 * 10^9 Joules (yikes ?)
Joules per second I mean (Watts)
To calculate the power wasted by the waterfall, we need to know the potential energy converted into kinetic energy. The formula to calculate the potential energy is:
Potential Energy (PE) = mass (m) x gravity (g) x height (h)
In this case, the height is given as 59 m, and the rate of flow of water is given as 2.1 × 10^6 kg/s. We can substitute these values into the formula:
PE = (2.1 × 10^6 kg/s) x (9.8 m/s^2) x (59 m)
Let's calculate the potential energy:
PE = 2.1 × 10^6 kg/s x 9.8 m/s^2 x 59 m
= 1225560000 J/s
Now, power (P) is the rate at which energy is transferred or converted, so we can calculate power by dividing the potential energy by time:
Power (P) = PE / time
However, we don't have the time given in this question, so we are assuming that the given value of 2.1 × 10^6 kg/s is the rate of flow per second. Therefore, we can directly use the potential energy as the power:
Power (P) = 1225560000 W
Therefore, the power wasted by the waterfall is 1225560000 Watts.