Calculate the magnitude of the drag force on a missile 63 cm in diameter cruising at 220 m/s at low altitude, where the density of air is 1.2 kg/m3. Assume C = 0.75.
To calculate the magnitude of the drag force on a missile, we can use the drag force equation:
Drag Force = 0.5 * A * Cd * ρ * V^2
where:
- Drag Force is the force of air resistance (in Newtons).
- A is the reference area or cross-sectional area of the missile (in square meters).
- Cd is the drag coefficient, which is a dimensionless quantity that depends on the shape of the object.
- ρ is the density of the air (in kg/m^3).
- V is the velocity of the missile (in meters per second).
Given:
- Diameter (d) of the missile = 63 cm = 0.63 m
- Radius (r) of the missile = 0.63 m / 2 = 0.315 m
- Velocity (V) of the missile = 220 m/s
- Density (ρ) of air = 1.2 kg/m^3
- Drag coefficient (Cd) = 0.75
Step 1: Calculate the cross-sectional area (A) of the missile.
A = π * r^2
A = π * (0.315 m)^2
A ≈ 0.314 m^2
Step 2: Plug in the values into the drag force equation.
Drag Force = 0.5 * A * Cd * ρ * V^2
Drag Force = 0.5 * 0.314 m^2 * 0.75 * 1.2 kg/m^3 * (220 m/s)^2
Step 3: Calculate the final result.
Drag Force ≈ 68,614 N
So, the magnitude of the drag force on the missile is approximately 68,614 Newtons.