Air Resistance Formula | Problems (And Solutions)

Air Resistance Formula

Drag force or Air resistance force (FD) is equal to half times the product of density (ρ), cross sectional area (A), drag coefficient (CD) and the square of velocity (v). Using the formula of air resistance: FD = ½ × ρ A CD v2, the value of air resistance force acting on a falling object can be calculated.

Let’s solve some problems based on this formula, so you’ll get a clear idea.

Air Resistance Practice Problems

Problem 1: Calculate the air resistance force acting on a feather falling with a velocity of 8 m/s. If the density of the air is 1.20 kg/m3, the cross sectional area of a feather is 0.02 m2, and the drag coefficient is 0.05.

Solution:

Given data:
Velocity of a feather, v = 8 m/s
Density of the air, ρ = 1.20 kg/m3
Cross sectional area of a feather, A = 0.02 m2
Drag coefficient, CD = 0.05
Air resistance force acting on a feather, FD = ?

Using the formula of air resistance,
FD = ½ × ρ A CD v2
FD = ½ × 1.20 × 0.02 × 0.05 × (8)2
FD = 0.03 N

Therefore, the air resistance force acting on a feather is 0.03 N.


Problem 2: When a skydiver jumps from a plane, a skydiver is falling with the velocity of 45 m/s. Calculate the air resistance force acting on a skydiver, if the density of the air is 1.25 kg/m3, the cross sectional area of a skydiver is 0.20 m2, and the drag coefficient is 0.70.

Solution:

Given data:
Velocity of a skydiver, v = 45 m/s
Density of the air, ρ = 1.25 kg/m3
Cross sectional area of a skydiver, A = 0.20 m2
Drag coefficient, CD = 0.70
Air resistance force acting on a skydiver, FD = ?

Using the formula of air resistance,
FD = ½ × ρ A CD v2
FD = ½ × 1.25 × 0.20 × 0.70 × (45)2
FD = 177.18 N

Therefore, the air resistance force acting on a skydiver is 177.18 N.


Problem 3: One leaf (floating in the air) is falling down from some height with the velocity of 10 m/s. If the density of the air is 1.22 kg/m3, the cross sectional area of a leaf is 0.05 m2, and the drag coefficient is 0.08, then find the value of the air resistance force acting on a leaf.

Solution:

Given data:
Velocity of a leaf, v = 10 m/s
Density of the air, ρ = 1.22 kg/m3
Cross sectional area of a leaf, A = 0.05 m2
Drag coefficient, CD = 0.08
Air resistance force acting on a leaf, FD = ?

Using the formula of air resistance,
FD = ½ × ρ A CD v2
FD = ½ × 1.22 × 0.05 × 0.08 × (10)2
FD = 0.24 N

Therefore, the air resistance force acting on a leaf is 0.13 N.


Problem 4: What is the value of the air resistance force acting on a parachute bag falling with the velocity of 30 m/s, when it is thrown from a helicopter? The density of the air is 1.21 kg/m3, the cross sectional area of a parachute bag is 0.10 m2, and the drag coefficient is 0.12.

Solution:

Given data:
Velocity of a parachute bag, v = 30 m/s
Density of the air, ρ = 1.21 kg/m3
Cross sectional area of a parachute bag, A = 0.10 m2
Drag coefficient, CD = 0.12
Air resistance force acting on a parachute bag, FD = ?

Using the formula of air resistance,
FD = ½ × ρ A CD v2
FD = ½ × 1.21 × 0.10 × 0.12 × (30)2
FD = 6.53 N

Therefore, the air resistance force acting on a parachute bag is 6.53 N.

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