Overview
This lecture explains the motion of objects in free fall, focusing on the effects of gravity and air resistance, and demonstrates how to solve key free fall problems using kinematic equations.
Free Fall and Gravity
- When two objects of different mass are dropped from the same height (with no air resistance), they hit the ground at the same time.
- Acceleration due to gravity on Earth is 9.8 m/sĀ² downward.
- Air resistance affects lighter objects with larger surface areas, causing them to fall slower.
- Crumpling a piece of paper reduces air resistance, making its fall time closer to that of a heavier object.
Speed, Velocity, and Acceleration in Free Fall
- Acceleration describes how fast velocity changes each second; for gravity, it's -9.8 m/sĀ² (downwards).
- Speed is always positive; velocity can be negative if the object moves downward.
- Every second, a falling object's speed increases by 9.8 m/s due to gravity.
Kinematic Equations for Free Fall
- For constant speed: ( d = v t ), where distance ( d ), velocity ( v ), time ( t ).
- For constant acceleration (such as free fall), use:
- ( v_f = v_i + a t )
- ( d = v_i t + \frac{1}{2} a t^2 )
- ( d = \frac{1}{2} (v_i + v_f) t )
- ( v_f^2 = v_i^2 + 2 a d )
- Distance is a scalar (always positive); displacement is a vector (can be negative).
Example Problems with Solutions
- Dropping a ball from rest: use ( v_f = v_i + a t ) for final velocity; speed is the absolute value of velocity.
- For displacement: use ( d = v_i t + \frac{1}{2} a t^2 ); sign indicates direction.
- If thrown downward, include initial velocity (( v_i )) as negative.
- For height of a building or cliff: calculate displacement during fall; report height as a positive value.
- To find time from height: solve ( d = \frac{1}{2} a t^2 ) for ( t ).
Key Terms & Definitions
- Free fall ā motion under the influence of only gravity.
- Acceleration due to gravity (g) ā 9.8 m/sĀ² downward on Earth.
- Speed ā how fast an object moves (always positive, scalar).
- Velocity ā speed with direction (can be positive or negative).
- Displacement ā change in position (vector, can be negative).
- Distance ā length traveled (always positive, scalar).
- Air resistance ā force opposing motion through air, increases with surface area.
Action Items / Next Steps
- Practice using each kinematic equation for free fall problems.
- Attempt similar homework questions involving objects dropped or thrown from heights.
- Review definitions of vector vs scalar quantities (velocity/displacement vs speed/distance).