How to Calculate Net Force of a Falling Object with Air Resistance

Net Force Equation:

\[ F_{net} = m g - F_{drag} \]

Mass (m):

Velocity (v):

m/s

Air Density (ρ):

kg/m³

Drag Coefficient (C_d):

(unitless)

Cross-sectional Area (A):

m²

Net Force (F_net):

Gravitational Force (mg):

Drag Force (F_drag):

Acceleration:

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1. What is Net Force of a Falling Object?

The net force on a falling object is the vector sum of all forces acting on it. For objects falling through air, this includes gravitational force (downward) and drag force (upward). Understanding net force helps predict motion and terminal velocity.

2. How Does the Calculator Work?

The calculator uses the net force equation:

\[ F_{net} = m g - F_{drag} \] \[ F_{drag} = \frac{1}{2} \rho v^2 C_d A \]

Where:

\( F_{net} \) — Net force (N)
\( m \) — Mass of the object (kg)
\( g \) — Gravitational acceleration (9.81 m/s²)
\( F_{drag} \) — Drag force (N)
\( \rho \) — Air density (kg/m³)
\( v \) — Velocity (m/s)
\( C_d \) — Drag coefficient (unitless)
\( A \) — Cross-sectional area (m²)

Explanation: The equation calculates the difference between gravitational force and air resistance, determining whether the object accelerates, decelerates, or reaches terminal velocity.

3. Importance of Net Force Calculation

Details: Calculating net force is essential for understanding object motion, predicting terminal velocity, designing parachutes, analyzing free-fall scenarios, and solving physics problems involving air resistance.

4. Using the Calculator

Tips: Enter mass in kilograms, velocity in m/s, air density in kg/m³ (default 1.225 for sea level), drag coefficient (default 0.47 for sphere), and cross-sectional area in m². All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is terminal velocity?
A: Terminal velocity occurs when net force equals zero (F_net = 0), meaning drag force equals gravitational force and acceleration stops.

Q2: How does air density affect falling objects?
A: Higher air density increases drag force, reducing net force and terminal velocity. At higher altitudes, lower density allows higher terminal velocities.

Q3: What are typical drag coefficients?
A: Sphere: 0.47, Streamlined body: 0.04-0.1, Flat plate: 1.28, Skydiver: 0.7-1.0, depending on orientation.

Q4: When is air resistance negligible?
A: For dense, small objects falling short distances, or at low velocities where drag force is much smaller than gravitational force.

Q5: How does net force relate to acceleration?
A: According to Newton's second law (F_net = m × a), net force divided by mass gives acceleration. Positive net force means downward acceleration.