Hydroelectricity is generated by storing water behind a dam, and then letting some of it run through generators in the dam to turn them. If the system is the water, what is the environment that is doing work on it? If a dam has water 100m deep behind it, how much energy was generated if 10,000kg of water exited the dam at 2m/s?
In the case of hydroelectricity generation, the environment that is doing work on the water is gravity. When water is stored behind a dam, it gains potential energy due to its elevated position. This potential energy is then converted into kinetic energy as the water flows downward through the generators in the dam. The force of gravity is what enables the water to move and perform work.
To calculate the amount of energy generated, we can use the formula:
Energy = (mass of water) x (acceleration due to gravity) x (change in height)
In this case, the mass of water exiting the dam is given as 10,000 kg and the exit velocity is 2 m/s. The change in height can be calculated by subtracting the height at which the water exits the dam from the height at which the water is stored behind the dam.
Given:
Mass of water (m) = 10,000 kg
Exit velocity (v) = 2 m/s
Height behind dam (h1) = 100 m
Exit height (h2) = 0 m (assuming water exits at ground level)
Change in height (Δh) = h1 - h2 = 100 m - 0 m = 100 m
Acceleration due to gravity (g) is approximately 9.8 m/s^2
Using the formula for energy, we can calculate:
Energy = (10,000 kg) x (9.8 m/s^2) x (100 m)
= 9,800,000 Joules
Therefore, approximately 9,800,000 Joules of energy were generated when 10,000 kg of water exited the dam at 2 m/s.