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.