Free-Falling Objects

Introduction to Free Fall

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.

• Definition: A free-falling object is one that is acted upon only by gravity.

• Key Assumption: Air resistance and friction are ignored.

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

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

Example: A ball thrown upward will eventually slow down, stop momentarily, and then accelerate downward under gravity.

Acceleration Due to Gravity

The acceleration experienced by free-falling objects is called the acceleration due to gravity, denoted by g. Near Earth's surface, this value is approximately constant.

• Standard Value:

• Vector Direction: If the upward direction is positive, then

• Sign Convention: Acceleration is negative when directed downward (toward Earth).

Example: An object dropped from rest will accelerate downward at .

States of Free-Falling Objects

Regardless of the initial velocity, all free-falling objects experience the same downward acceleration due to gravity.

• Object moving upward: Acceleration is downward ().

• Object at rest: Acceleration is downward ().

• Object moving downward: Acceleration is downward ().

Equations for Linear Free Fall

Kinematic Equations for Free Fall

When analyzing free-fall motion, we use kinematic equations with constant acceleration. If the positive y-axis is defined as upward, then .

• Equation 1 (Linear):

• Equation 2 (Parabolic):

• Equation 3:

These equations relate the following quantities:

Additional info: The table above summarizes which variables each equation can solve for, based on the context of free-fall motion.

Sign Convention and Coordinate System

It is important to define the coordinate system when solving free-fall problems. Typically, upward is taken as positive, making the acceleration due to gravity negative.

• Downward acceleration:

• Negative sign: Indicates direction toward Earth.

Applications and Examples

• Example 1: A ball thrown upward slows down under gravity, stops momentarily, then accelerates downward.

• Example 2: An object dropped from rest accelerates downward at .

Summary: Free-fall motion is a fundamental concept in physics, describing the vertical motion of objects under gravity. The acceleration due to gravity is nearly constant near Earth's surface, and the kinematic equations allow us to predict position and velocity at any time.