Overview
The lecture explains how to draw free body diagrams for various physical situations, focusing on identifying and representing all forces acting on an object.
Drawing Free Body Diagrams: Basics
- A free body diagram shows all forces acting on a single object.
- Arrows represent forces; their length reflects the magnitude, and direction shows action.
Common Forces in Diagrams
- Weight force (W) or gravity always acts downward: ( W = mg ).
- Normal force (N) is perpendicular to surfaces and supports objects resting on them.
- Tension (T) acts along ropes or cables.
- Friction opposes motion; kinetic friction (( f_k )) if moving, static friction (( f_s )) if at rest.
- Applied force (( F_{app} )) is any external push or pull._
Sample Situations & Key Points
- Box on Table (at rest): Upward normal force equals downward weight; arrows equal length.
- Block hanging from rope: Tension upward equals weight downward if at rest.
- Block pulled upward (constant velocity): Tension equals weight—no acceleration.
- Block pulled upward (constant acceleration): Tension > weight; ( T = mg + ma ).
- Block descending (acceleration): Weight > tension; net force downward.
Horizontal Motion Examples
- Frictionless surface, constant speed: Only normal and weight forces; no horizontal forces.
- Applied force at constant speed (with friction): Applied force equals kinetic friction (( F_{app} = f_k )).
- Applied force with acceleration (with friction): Applied force > kinetic friction; net force causes acceleration.
- Rope pulls block at constant velocity (with friction): Tension right equals kinetic friction left (( T = f_k )).
- Rope pulls at 30° angle (with friction, acceleration): Tension has both x and y components; normal force reduced by vertical tension component._
Inclined Plane Situations
- Frictionless incline: Forces: weight (down), normal (perpendicular), gravity component down slope (( mg\sin\theta )); acceleration ( a = g\sin\theta ).
- Block at rest on incline (with friction): Static friction balances downslope gravity; ( f_s = mg\sin\theta ), up to maximum ( \mu_s N ).
- Sliding down incline (with kinetic friction): Acceleration ( a = g\sin\theta - \mu_k g\cos\theta ).
- Pulling up incline at constant velocity: Tension balances kinetic friction; ( T = \mu_k mg\cos\theta ).
Key Terms & Definitions
- Free Body Diagram — A visual showing all forces on an object.
- Weight (W) — Force due to gravity (( mg )).
- Normal Force (N) — Support force perpendicular to contact surface.
- Tension (T) — Force transmitted through a rope/cable.
- Applied Force (( F_{app} )) — External force exerted on an object.
- Static Friction (( f_s )) — Force resisting motion start (( \leq \mu_s N )).
- Kinetic Friction (( f_k )) — Force resisting ongoing motion (( = \mu_k N ))._
Action Items / Next Steps
- Practice drawing free body diagrams for new situations.
- Review formulas for force components and friction.
- Complete assigned homework on free body diagrams.