Air Resistance and Speed Relationship Notes

Air Resistance and Car Speed Relationship

• Objective: Investigate how air resistance varies with speed for a car and determine a functional relationship graphically.

• Convert Speed:

  • Conversion Factor: 1 km/h = ( \frac{1}{3.6} ) m/s.

  • Conversion for each speed:

  • 20 km/h = ( \frac{20}{3.6} \approx 5.56 ) m/s

  • 30 km/h = ( \frac{30}{3.6} \approx 8.33 ) m/s

  • 40 km/h = ( \frac{40}{3.6} \approx 11.11 ) m/s

  • 50 km/h = ( \frac{50}{3.6} \approx 13.89 ) m/s

  • 60 km/h = ( \frac{60}{3.6} \approx 16.67 ) m/s

  • 70 km/h = ( \frac{70}{3.6} \approx 19.44 ) m/s

  • 80 km/h = ( \frac{80}{3.6} \approx 22.22 ) m/s

  • 90 km/h = ( \frac{90}{3.6} \approx 25.00 ) m/s

  • 100 km/h = ( \frac{100}{3.6} \approx 27.78 ) m/s

• Air Resistance Data: (Coefficient of air resistance in newtons)

  • Speed (m/s) vs Air Resistance (N)

  • 5.56 m/s - 370 N

  • 8.33 m/s - 833 N

  • 11.11 m/s - 1481 N

  • 13.89 m/s - 2315 N

  • 16.67 m/s - 3333 N

  • 19.44 m/s - 4537 N

  • 22.22 m/s - 5926 N

  • 25.00 m/s - 7500 N

  • 27.78 m/s - 9259 N

• Graphical Representation:

  • Plot the air resistance measurements (y-axis) against the car's speed in meters per second (x-axis).

  • Observe the trend in the graph: typically, as speed increases, air resistance also increases, often following a quadratic or polynomial relationship.

• Determine Mathematical Relationship:

  • By analyzing the graph, you can determine the nature of the relationship (linear, quadratic, etc.)

  • If needed, additional calculations like finding the best-fit line or curve may be performed to quantify the relationship.

• Considerations for Analysis:

  • Factors affecting air resistance: shape of the car, density of the air, and velocity of the car.

  • Importance of aerodynamic design in reducing air resistance.