Freely Falling Objects (Gravity)

Introduction to Free Fall

Free fall describes the motion of objects under the influence of gravity alone, with negligible air resistance. This is a fundamental topic in introductory physics, illustrating the application of kinematic equations to vertical motion.

• Free fall is a special case of motion with constant acceleration, where the only force acting is gravity.

• The acceleration due to gravity is denoted by g, and its standard value near Earth's surface is .

• In free fall, the acceleration is always directed downward, regardless of the object's initial motion.

• When air resistance is negligible, all objects fall with the same acceleration, regardless of mass.

Kinematic Equations for Constant Acceleration

The following equations describe the motion of objects with constant acceleration, including free fall:

• Final velocity:

• Displacement:

• Velocity-displacement relation:

For free fall, replace with (downward acceleration) and use for vertical displacement:

Types of Free Fall Problems

There are three main scenarios for free fall:

• Dropping an object: Initial velocity .

• Throwing an object upward: Initial velocity (upward, positive direction).

• Throwing an object downward: Initial velocity (downward, negative direction).

Example Table: Free Fall Scenarios

Key Concepts and Definitions

• Initial velocity (): The velocity of the object at the start of the motion.

• Acceleration due to gravity (): The constant rate at which objects accelerate downward, .

• Displacement (): The vertical distance moved by the object.

• Maximum height: The highest point reached by an object thrown upward, where instantaneous velocity .

Special Cases and Catchwords

Recognizing certain phrases in problems helps identify initial or final conditions:

• "from rest" or "from release" implies

• "uniform acceleration" implies

• "free fall" implies

• "the highest point" implies

• "comes to a stop" implies

Examples and Applications

• Example 1: Dropping a Ball A ball is dropped from rest () from a height. Its position after time is given by .

• Example 2: Throwing a Ball Upward A ball is thrown upward with initial velocity . It rises until its velocity becomes zero at the maximum height, then falls back down. The time to reach maximum height is .

• Example 3: Free Fall in a Vacuum vs. Air In a vacuum, all objects fall at the same rate regardless of mass or shape. With air resistance, lighter or less aerodynamic objects fall more slowly.

Physics in Action: Stunt Jumps and Free Fall

• Stunt performers jumping from great heights experience free fall. The impact speed can be calculated using (with and negative for downward displacement).

• Air resistance reduces the final speed compared to the idealized case of free fall in a vacuum.

Summary Table: Free Fall Key Points

Additional info: In real-world scenarios, air resistance can significantly affect the motion of falling objects, especially for objects with large surface areas or low mass. However, for most introductory physics problems, air resistance is neglected unless otherwise specified.