Water flows over Victoria Falls, which is 128 m high, at a rate of 1.4 x 106 kg/s. If half the potential energy of this water were converted into electric energy, how much electric power would be produced by these falls?
(1/2)(mass flow rate)*(K.E. per mass at impact)
= (1/2)*(mass flow rate)*V^2/2
= (1/4)*(mass flow rate)*g*H
is the answer 439040000W ?
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To calculate the electric power generated by the falls, we need to first determine the amount of potential energy being converted. The potential energy is given by the formula:
Potential Energy = mass x gravity x height
where:
mass = 1.4 x 10^6 kg/s (rate of water flow)
gravity = 9.8 m/s^2 (acceleration due to gravity)
height = 128 m (height of Victoria Falls)
Plugging in these values:
Potential Energy = (1.4 x 10^6 kg/s) x (9.8 m/s^2) x (128 m)
Now we need to find half of this potential energy (since only half is being converted). We can simply divide the total potential energy by 2:
Total Potential Energy = (1.4 x 10^6 kg/s) x (9.8 m/s^2) x (128 m)
Half of Potential Energy = Total Potential Energy / 2
Next, to find the electric power produced, we need to consider the time it takes for this potential energy to be converted. Let's assume that all the potential energy is converted in 1 second, so the time is 1s.
Electric Power = Half of Potential Energy / Time
Plugging in the values:
Electric Power = [(1.4 x 10^6 kg/s) x (9.8 m/s^2) x (128 m)] / 2 / 1 s
Now we can calculate the result:
Electric Power = (1.4 x 10^6 kg/s) x (9.8 m/s^2) x (128 m) / 2
Calculating this expression gives us the electric power generated by the falls.