Question
A remote village in the UK uses a hydroelectric generator to provide electricity. In one day, 2500 000 kg of water passes through the hydroelectric generator. The change in gravitational potential energy of the water is 367.5 MJ. gravitational field strength=9.8N/kg Calculate the mean change in vertical height of the water as it moves through the hydroelectric generator. Use the Physics Equations Sheet. [4 marks __
Answer
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(219 Votes)
Ulysses
Elite · Tutor for 8 years
Answer
The mean change in vertical height of the water as it moves through the hydroelectric generator is 15 m.
Explanation
1. The formula to calculate the change in gravitational potential energy (ΔU) is
, where: -
is the mass of the object. -
is the gravitational field strength. -
is the change in height.2. From the question, we know that: - The mass that moves through the hydroelectric generator
, - The change in gravitational potential energy
(converted from MJ to J), because we need to maintain units consistency in the formula. - Gravitational field strength
.3. We can rearrange the formula to find the change in height
: \( Δh = ΔU / (m \times g) \).4. Substituting the known values in the rearranged formula gives \( Δh = 367.5 \times 10^6 \mathrm{~J} / (2500000 \mathrm{~kg} \times 9.8 \mathrm{~N} / \mathrm{kg}) \).5. The calculation gives the mean change in vertical height of the water as it moved through the hydroelectric generator by about
.