Air Resistance Formula - Definition, Formula, Solved Examples

Air Resistance Formula: Air resistance, often referred to as drag, is the force that opposes the motion of an object as it moves through the air. It's a result of the interaction between the air and the surface of the moving object. In simpler terms, it's what slows down a car on the highway, a parachute during descent, and a soccer ball in flight.

Understanding the Physics Behind Air Resistance Formula

Air Resistance Formula

Where:

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Factors Affecting Air Resistance Formula

Practical Applications:

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Air Resistance Formula Solved Examples

F = 0.5 * ρ * A * Cd * v^2

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Now, we can calculate F:

F = 0.5 * 1.225 kg/m³ * 0.0042 m² * 0.47 * (50 m/s)^2

F ≈ 6.03 N

F_gravity = F

1.421 N = 6.03 N

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Solution:

F_gravity = m * g

F_gravity = 0.145 kg * 9.8 m/s² = 1.421 N

F = 0.5 * ρ * A * Cd * v^2

F = 0.5 * 1.225 kg/m³ * 0.0042 m² * 0.47 * (50 m/s)^2

F ≈ 6.03 N

F_gravity = F

1.421 N = 6.03 N

*Problem*: A racing car with a mass of 800 kg is moving at a speed of 180 km/h. Calculate the force of air resistance acting on the car.

Solution:

F = 0.5 * ρ * A * Cd * v^2

*Assuming:*

F = 0.5 * 1.225 kg/m³ * 2.0 m² * 0.3 * (50 m/s)^2

F ≈ 918.75 N

Solution:

F_gravity = m * a

600 N = m * a

a = 600 N / m

a = g

600 N / m = 9.8 m/s²

m = 600 N / 9.8 m/s² ≈ 61.22 kg

F_net = F_gravity - F

F_net = 600 N - 500 N = 100 N

F_net = m * a

100 N = 61.22 kg * a

a ≈ 1.63 m/s²

v = √(2 * a * s)

Solution:

F = 0.5 * ρ * A * Cd * v^2

*Assuming:*

F = 0.5 * 1.225 kg/m³ * 0.5 m² * 0.9 * (20 m/s)^2

F ≈ 220.5 N

Solution:

v_terminal = √(2 * m * g / (ρ * A * Cd))