Lecture Notes: Freely Falling Objects

Introduction to Free Fall

• Definition: An object is in free fall if it's only influenced by gravity.
  • No other forces acting on it (e.g., air resistance, buoyancy).
• Examples: A heavy ball and feathers in a vacuum fall at the same rate.

Acceleration Due to Gravity

• Standard acceleration: 9.8 meters per second squared (m/s²) downward.
• In class, we use: 9.81 m/s².
• Acts towards the center of the Earth.
• Mass and size do not affect the rate of fall.

Examples of Free Fall

1. Dropped Objects

• Initial velocity = 0.
• Objects like an elephant and a coin fall with same acceleration (9.8 m/s²).

2. Objects with Non-Zero Initial Velocity

• Example: Cannon shooting downward.
  • Initial speed: 3 m/s.
  • Velocity increases as it falls (vector grows); acceleration remains constant.

3. Pop-Up (Thrown Upwards)

• Objects thrown upwards are also in free fall immediately after leaving the hand.
• Initial velocity (v₀) is positive.
• Gravity decreases upward velocity until it reaches zero (maximum height), then increases as it falls back down.

Motion Graphs for Free Fall

Position vs. Time

• Initial velocity creates a rise (upwards motion) until maximum height is reached.
• Symmetry around maximum height in the graph.

Velocity vs. Time

• Starts at initial velocity (v₀), decreases to zero at max height.
• Continues decreasing (negative) as the object falls back down.
• Symmetry in velocity at each point up/down the path.

Acceleration vs. Time

• Constant: 9.8 m/s² downwards.

Symmetry in Motion

• Velocity symmetry: At any height, object has the same speed going up as going down, but with opposite signs.
• Example: Thrown at 29.4 m/s up, comes down at -29.4 m/s.
• At each point: Speed is the same, velocity differs in direction.

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These notes provide a summary of key concepts related to freely falling objects, illustrating how gravity affects motion irrespective of an object's mass or size.