The UK uses renewable energy resources to generate some of its electricity - AQA - GCSE Physics - Question 4 - 2023 - Paper 1

The gravitational potential energy (E_p) can be calculated using the formula:

$E_p = \text{mass} \times \text{gravitational field strength} \times \text{height}$

Substituting the provided values:

$E_p = 2 500 000 \, \text{kg} \times 9.8 \, \text{N/kg} \times 15.0 \, \text{m}$

$E_p = 367 500 000 \, \text{J}$

Thus, the decrease in gravitational potential energy of the water is 367,500,000 J.

The equation that links energy (E), power (P), and time (t) is:

$E = P \times t$

First, convert the time into seconds:

$t = 60 \, \text{minutes} \times 60 \, \text{seconds/minute} = 3600 \, \text{s}$

Now, using the power of the generator (3000 W):

$E = P \times t = 3000 \, \text{W} \times 3600 \, \text{s} = 10 800 000 \, \text{J}$

Therefore, the energy transferred to the village is 10,800,000 J.

One reason the power output varied is that the level of the water in the river changes, influenced by factors such as rainfall or seasonal variations. This can lead to fluctuations in the amount of water available to turn the hydroelectric generator.