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Problem 4: 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. Randomized Variables h = 51 m 33% Part (a) Consider a penstock that is vertical and has a height of h = 51 m. How long, t in seconds, does it take water to fall from the top of the penstock to the bottom? Assume the water starts at rest. 33% Part (b) How much total mechanical energy, Ew in Joules, does a mass of 1kg of water have when it reaches the generator? 33% Part (c) Assume the water interacts with the generator for 10% of the time it took to fall. If it is at rest just before it exits the generator, how much power, P in Watts, does the water produce?

          Problem 4: 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.

Randomized Variables
h = 51 m

33% Part (a) Consider a penstock that is vertical and has a height of h = 51 m. How long, t in seconds, does it take water to fall from the top of the penstock to the bottom? Assume the water starts at rest.

33% Part (b) How much total mechanical energy, Ew in Joules, does a mass of 1kg of water have when it reaches the generator?
33% Part (c) Assume the water interacts with the generator for 10% of the time it took to fall. If it is at rest just before it exits the generator, how much power, P in Watts, does the water produce?

Problem 4: 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.

Randomized Variables
h = 51 m

33% Part (a) Consider a penstock that is vertical and has a height of h = 51 m. How long, t in seconds, does it take water to fall from the top of the penstock to the bottom? Assume the water starts at rest.

33% Part (b) How much total mechanical energy, Ew in Joules, does a mass of 1kg of water have when it reaches the generator?
33% Part (c) Assume the water interacts with the generator for 10% of the time it took to fall. If it is at rest just before it exits the generator, how much power, P in Watts, does the water produce?

Added by Juan Manuel W.

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