Free Fall with Air Resistance Calculator

Calculate the motion of objects falling through air with resistance

Free Fall with Air Resistance Calculator

Enter the mass of the object

Enter the initial height

Enter the drag coefficient (e.g., 0.47 for a sphere)

Enter the cross-sectional area perpendicular to motion

How Free Fall with Air Resistance Works

Free fall with air resistance is a more realistic model of falling objects compared to ideal free fall. When an object falls through air, it experiences two main forces:

  • Gravitational Force: A constant downward force equal to the object's mass times the acceleration due to gravity (mg).
  • Air Resistance (Drag Force): An upward force that increases with velocity and depends on the object's shape, size, and the properties of the air.

As the object falls, it eventually reaches terminal velocity when these forces balance each other, resulting in constant speed.

Factors Affecting Free Fall with Air Resistance
  • Mass: Affects the gravitational force and the object's acceleration.
  • Cross-sectional Area: Larger area means more air resistance.
  • Drag Coefficient: Depends on the object's shape and surface properties.
  • Air Density: Changes with altitude and affects the magnitude of air resistance.
  • Initial Height: Determines the total distance and time of fall.
Key Equations and Concepts

The main equations governing free fall with air resistance are:

  • Drag Force: Fd = ½ρCv²A
    Where: ρ = air density, C = drag coefficient, v = velocity, A = cross-sectional area
  • Terminal Velocity: vt = √(2mg/ρCA)
    Where: m = mass, g = acceleration due to gravity
  • Net Force: Fnet = mg - Fd
Real-world Applications
  • Skydiving: Calculating safe descent rates and equipment design
  • Weather Balloons: Predicting descent paths and landing locations
  • Sports: Analyzing ball trajectories in various games
  • Engineering: Designing parachutes and air-drop systems
  • Safety Testing: Analyzing fall protection equipment
Frequently Asked Questions

What is terminal velocity and why is it important?

Terminal velocity is the constant speed reached when the upward air resistance equals the downward gravitational force. It's the maximum speed an object can achieve during free fall in air.

How does air resistance affect falling objects?

Air resistance opposes motion, causing objects to fall slower than they would in a vacuum. The effect increases with speed until terminal velocity is reached.

Why do different objects fall at different rates in air?

Objects fall at different rates due to variations in their mass-to-area ratio, shape (drag coefficient), and other properties that affect air resistance.