Question

two pumped hydro systems, a and b, are shown by simple models. determine the amount of potential energy stored in each system and explain why one system has more stored energy. system a: 240 kg water, upper reservoir, 700 m to lower reservoir, g = 9.8 m/s². system b: 520 kg water, upper reservoir, 300 m to lower reservoir, g = 9.8 m/s².

Explanation:

Step1: Recall Potential Energy Formula

The formula for gravitational potential energy is \( PE = mgh \), where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is height.

Step2: Calculate PE for System A

For System A: \( m = 240 \, \text{kg} \), \( g = 9.8 \, \text{m/s}^2 \), \( h = 700 \, \text{m} \).
Substitute into the formula:
\( PE_A = 240 \times 9.8 \times 700 \)
\( PE_A = 240 \times 6860 \)
\( PE_A = 1646400 \, \text{J} \)

Step3: Calculate PE for System B

For System B: \( m = 520 \, \text{kg} \), \( g = 9.8 \, \text{m/s}^2 \), \( h = 300 \, \text{m} \).
Substitute into the formula:
\( PE_B = 520 \times 9.8 \times 300 \)
\( PE_B = 520 \times 2940 \)
\( PE_B = 1528800 \, \text{J} \)

Step4: Compare Energies

Compare \( PE_A \) and \( PE_B \). \( 1646400 \, \text{J} > 1528800 \, \text{J} \), so System A has more stored energy. This is because even though System B has more mass, System A has a significantly greater height, and potential energy depends on both mass and height (with height having a large impact here).

Answer:

• Potential Energy of System A: \( 1646400 \, \text{J} \)
• Potential Energy of System B: \( 1528800 \, \text{J} \)
• System A has more stored energy because \( PE = mgh \), and the product \( m \times h \) for A (\( 240 \times 700 = 168000 \)) is greater than for B (\( 520 \times 300 = 156000 \)), leading to higher \( PE \).