Air resistance formula

Air resistance formula, also known as the drag force formula, calculates the force experienced by an object moving through a fluid medium, such as air. It is represented by the equation FD = ½ × ρ A CD v2, where FD is the drag force, ρ is the density of the fluid, A is the cross-sectional area of the object, CD is the drag coefficient, and v is the velocity of the object.

Contents

Practice problems

Problem #1

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

Solution

Given data:

• Air resistance force acting on a feather, FD = ?
• 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

Applying the formula:

• 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, the skydiver falls with a velocity of 45 m/s. Determine the air resistance force acting on the skydiver, considering the density of the air as 1.25 kg/m3, the cross-sectional area of the skydiver as 0.20 m2, and the drag coefficient as 0.70.

Solution

Given data:

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

Applying the formula:

• 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

A leaf is descending from a certain height with a velocity of 10 m/s while floating in the air. Find the air resistance force acting on the leaf, taking into account the density of the air as 1.22 kg/m3, the cross-sectional area of the leaf as 0.05 m2, and the drag coefficient as 0.08.

Solution

Given data:

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

Applying the formula:

• 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

Find the value of the air resistance force acting on a parachute bag that is falling with a velocity of 30 m/s after being thrown from a helicopter. Given the density of the air as 1.21 kg/m3, the cross-sectional area of the parachute bag as 0.10 m2, and the drag coefficient as 0.12.

Solution

Given data:

• Air resistance force acting on a parachute bag, FD = ?
• 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

Applying the formula:

• 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.