Question

A dam collects water at a height of 300m. The water can be let down through a pipe. As it falls to the ground it loses potential energy but it gains kinetic energy. 100 tonnes (note 1 tonne 1000 kg) of water are let out from the dam and reach the ground, 300m below; all the gained kinetic energy is then harnessed by a perfectly efficient turbine and converted into energy to power houses in the valley. The Bureau of Statistics tells us that an average household consumes approximately 500 MJ of energy per week (note: M stands for million, so MJ is one million Joules). (a) How many houses can be powered by the falling water for an hour? (b) If the same amount of water came down at a slow rate of 1 kg/h what would be the power output of the dam? [We should use 2 s.f. for this problem].

Answer 1

Energy of 100 tonnes of water

mass of water = 100*1000 = 10^5 kg

Height = 300m

Energy = mass*height*acceleration due to gravity

E = 100000*300*10 = 300000000 = 3 * 10^8 J

1 MJ = 10^6 J

So, Energy = 300MJ

a) Number of houses powered = 300/50 = 6

b) Power output = energy of water = mgh = 1*10*300 = 3000J/hr