Free-Falling Objects

Definition and Characteristics

Free-falling objects are those that move vertically under the sole influence of gravity, with air resistance and friction neglected. This idealization allows us to study the fundamental effects of gravity on motion.

• Free fall occurs when an object is acted upon only by gravity.

• The acceleration due to gravity is denoted by g and is approximately constant near Earth's surface.

• Standard value:

• Direction: Acceleration due to gravity always points toward the center of the Earth.

• Altitude effect: The value of g decreases slightly with altitude (e.g., it is less at 10,000 m above sea level than at the surface).

• Coordinate system: The sign of g depends on how the coordinate system is defined (usually negative if upward is positive).

Example: A ball thrown upward will decelerate at until it stops and then accelerates downward at the same rate.

Acceleration Due to Gravity

Direction and Magnitude

The acceleration of a free-falling object is always directed downward and has a magnitude of .

• Equation:

• If the object is moving upward, its acceleration is still downward.

• If the object is instantaneously at rest (at the peak of its trajectory), its acceleration is still downward.

• If the object is moving downward, its acceleration remains downward.

Example: A ball thrown upward slows down due to negative acceleration, stops momentarily, and then accelerates downward.

Equations for Linear Free Fall

Kinematic Equations and Their Applications

When analyzing free-fall motion, we use kinematic equations that relate position, velocity, and time under constant acceleration.

• Coordinate system: If the y-axis points up, then .

• Key equations:

  • Linear equation:

  • Parabolic equation:

  • Velocity-position relation:

• Each equation allows solving for different combinations of variables (time, position, initial position, initial velocity, final velocity).

Example: Use to find the position of a ball after 2 seconds if thrown upward with initial velocity .

Additional info:

• These notes are foundational for understanding projectile motion, which builds on the principles of free fall by adding horizontal motion.

• In all cases, neglecting air resistance is an idealization; real-world scenarios may require corrections.