When calculating the energy in a tidal reservoir, when do we use the average height of the water (half the max tidal height) instead of the maximum tidal height in
E=mgh?
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Imagine you have a resevoir that is 100m high. In it you have only two particles. One at 25m and the other at 75m.
The total potential energy of these two particles is the same as having two particles at 50m.
The only value that changes in the calculation is h (the height of the particle above the ground).
So for every pair of particles, if you add up the h value and the total equals the height of the resevoir, it is the equivalent of having two particles at half the height of the resevoir (which is the average height of all the particles within it).
So if you take your resevoir, you have two choices. You can either calculate the value of PE for each particle at each seperate height or you can assume every particle to be at the average height and use the overall mass of all the particles. Which is easier?