Question

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.
h = 61 m

a.) Consider a penstock that is vertical and has a height of h = 61 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.

b.)How much total mechanical energy in houles does a mass of 1 kg of water have when it reaches the generator?

Answer 1

Answer:

Explanation:

In hydroelectric power , potential energy is converted into electrical energy

height given h = 61 m .

acceleration due to gravity g = 9.8

using the relation

h = ut + 1/2 gt²  , t is time taken to reach the bottom .

61 = 1/2 x 9.8 x t²

t² = 12.49

t = 3.53 s

b )

when a mass of 1 kg of water reaches the bottom , its potential energy will be converted into mechanical energy ( kinetic energy )

potential energy = mgh

m = mass of water = 1 kg

acceleration due to gravity g = 9.8

h = 61 m

potential energy = 1 x 9.8 x 61

= 597.8 J .

mechanical energy = 597.8 J .