Hydroelectric power plants convert the gravitational potential energy of falling water into electrical power, typically by allowing the water to flow through a pipe called a penstock to rotate a generator located below it. Let the bottom of the penstock be the origin of a Cartesian coordinate system and the point
Hydroelectric power plants convert the gravitational potential energy of falling water into electrical power, typically by allowing the water to flow through a pipe called a penstock to rotate a generator located below it. Let the bottom of the penstock be the origin of a Cartesian coordinate system and the point at which the gravitational potential energy is zero.
Consider a penstock that is vertical and has a height of h=84.5mh=84.5m. How long, in seconds, does it take water to fall from the top of the penstock to the bottom? Assume the water starts at rest.
How much total mechanical energy, in joules, does a mass of 1.00kg1.00kg of water have when it reaches the generator?
Assume the water interacts with the generator for ten percent (10.0%10.0%) of the time it took to fall. If it is at rest just before it exits the generator, how much power, in watts, does the water produce?
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