Assuming 100% efficient energy conversion, how much water stored behind a 50cm high hydroelectric dam would be required to charge a 50 ampere-minute 12 volt battery with 600j of energy stored in it

12.245m3

Explanation:

The electric energy is created by The potential energy substended by the specific volume of water in dam.

Electric energy is calculated as

E = Q * V

E is Energy, Q is charge and V is Voltage

Note that this energy has been given and is 60Joules

From conservation of energy it means;

M * g*h = 60

Where M is the mass of water.

g is acceleration of free fall due to gravity which is 9.8m/S2

h is the height of water flow.

From change of subject of formula for M; we have:

M = 60 / g * h

= 60 / 9.8 * 0.5

= 12.245kg

Now how much water required means the volume of water;

Note density = mass/volume

Therefore volume = mass/density

=12.245/1 = 12.245m3

Note the density of water is 1kg/m3