Question

In a hydroelectric dam, water falls 30.0m and then spins a turbine to generate electricity.

a) What is ?U of 1.0 kg of water?
Express your answer with the appropriate units.
Part B
Suppose the dam is 80% efficient at converting the water's potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 54.0MW of electricity? This is a typical value for a small hydroelectric dam.
Express your answer using three decimal places.

Answer 1

Answer:

(a) 294 J

(b) 229591.84 kg

Explanation:

height, h = 30 m

g = 9.8 m/s^2

(a) U = m x g x h

U = 1 x 9.8 x 30

U = 294 J

(b) Let the mass of water is m

U = m x g xh

80% of this energy per second is generating power

0.8 x m x 9.8 x 30 = 54 x 10^6

m = 229591.84 kg

Thus, the mass of water required is 229591.84 kg.