Solution: Coldplay Concert Energy Calculation

Step-by-Step Calculation

1. Energy from Kinetic Dance Tiles

Data given:

• Number of tiles: 60
• Power generated per tile: 40 W
• Percentage of attendees using tiles: 15% of 50,000 = 7,500 people
• Time spent on tiles: 1.5 hours = 1.5 × 3600 seconds = 5400 seconds

Formula:

\( E = P \times t \times \text{number of tiles} \)

Calculation:

\( E = 40 \, \text{W} \times 5400 \, \text{seconds} \times 60 = 12,960,000 \, \text{Joules} \)

Converting to kWh:

\( E = \frac{12,960,000}{3,600,000} = 3.6 \, \text{kWh} \)

2. Energy from Stationary Bicycles

Data given:

• Number of bicycles: 20
• Power generated per bicycle: 120 W
• Time used: 2.5 hours

Formula:

\( E = P \times t \times \text{number of bicycles} \)

Calculation:

\( E = 120 \, \text{W} \times 2.5 \, \text{hours} \times 20 = 6,000 \, \text{Wh} = 6 \, \text{kWh} \)

3. Energy from Solar Panels

Data given:

• Total solar panel area: 200 m²
• Solar irradiance: 700 W/m²
• Sunlight hours: 6 hours

Formula:

\( E = \text{Area} \times \text{Irradiance} \times t \)

Calculation:

\( E = 200 \, \text{m}^2 \times 700 \, \text{W/m}^2 \times 6 \, \text{hours} = 840,000 \, \text{Wh} = 840 \, \text{kWh} \)

4. Energy from Portable Wind Turbines

Data given:

• Number of turbines: 10
• Wind speed: 6 m/s
• Blade radius: 2 m
• Time operating: 3 hours
• Air density: \( \rho = 1.225 \, \text{kg/m}^3 \)

Formula:

\( P = 0.5 \times \rho \times A \times v^3 \)

Where \( A = \pi \times r^2 \)

Calculation:

\( A = \pi \times (2)^2 = 12.57 \, \text{m}^2 \)

\( P = 0.5 \times 1.225 \times 12.57 \times (6)^3 = 1,660.3 \, \text{W/turbine} \)

For 10 turbines operating for 3 hours:

\( E = 1,660.3 \times 10 \times 3 = 49,809 \, \text{Wh} = 49.8 \, \text{kWh} \)

5. Energy from Piezoelectric Stage Floor

Data given:

• Stage area: 100 m²
• Power generated per square meter: 50 W
• Percentage of time active: 80%
• Concert duration: 3 hours

Formula:

\( E = P \times \text{Area} \times \text{active time} \)

Calculation:

\( E = 50 \, \text{W/m}^2 \times 100 \, \text{m}^2 \times 0.8 \times 3 \, \text{hours} = 12,000 \, \text{Wh} = 12 \, \text{kWh} \)

6. Energy from Hydrogen Fuel Cell

Data given:

• Total energy: 30 kWh
• Efficiency: 50%

Formula:

\( E = 30 \times 0.5 \, \text{kWh} \)

Calculation:

\( E = 15 \, \text{kWh} \)

7. Energy from Thermal Energy of Attendees

Data given:

• Number of attendees: 50,000
• Energy generated per person: 0.1 kWh/hour
• Concert duration: 3 hours

Formula:

\( E = \text{attendees} \times 0.1 \, \text{kWh/person/hour} \times \text{time} \)

Calculation:

\( E = 50,000 \times 0.1 \times 3 = 15,000 \, \text{kWh} \)

8. Energy from Sound Energy Capture

Data given:

• Number of attendees: 50,000
• Energy captured per person: 0.005 kWh/person

Formula:

\( E = 0.005 \, \text{kWh/person} \times \text{attendees} \)

Calculation:

\( E = 0.005 \times 50,000 = 250 \, \text{kWh} \)

Total Energy Generated

Summing up all the energy generated:

\( E_{\text{total}} = 3.6 + 6 + 840 + 49.8 + 12 + 15 + 15,000 + 250 = 16,176.4 \, \text{kWh} \)

Comparison with Energy Consumption

Estimated energy consumption: 800 kWh

Total energy generated: 16,176.4 kWh

Conclusion: The concert generates far more energy than it consumes.