Water flows over a section of Niagara Falls at a rate of 1.20 × 106 kg/s and falls 55.0 m. What is the power dissipated by the waterfall?Select one:a.546.8 MWb.646.8 MWc.746.8 MWd.66 MWe.46 MW
Question
Water flows over a section of Niagara Falls at a rate of 1.20 × 106 kg/s and falls 55.0 m. What is the power dissipated by the waterfall?Select one:a.546.8 MWb.646.8 MWc.746.8 MWd.66 MWe.46 MW
Solution
The power dissipated by the waterfall can be calculated using the formula for power in physics, which is work done per unit time. In this case, the work done is the gravitational potential energy converted into kinetic energy as the water falls, which is given by the formula mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the fall.
Given: Mass flow rate (m) = 1.20 × 10^6 kg/s Height (h) = 55.0 m Acceleration due to gravity (g) = 9.81 m/s^2
Substituting these values into the formula:
Power = mgh = (1.20 × 10^6 kg/s)(9.81 m/s^2)(55.0 m) = 6.468 × 10^8 W = 646.8 MW
So, the power dissipated by the waterfall is 646.8 MW. Therefore, the correct answer is (b) 646.8 MW.
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