Fundamental Forces in Mechanics

Overview

This lecture covers fundamental forces in mechanics (normal, tension, friction), Newton's laws of motion, and how to analyze forces using free body diagrams, with example problems involving inclined planes and friction.

Types of Forces and Their Directions

• Normal force is a contact force exerted by a surface on an object, always perpendicular to the surface.
• On flat surfaces, normal force acts upward; on inclined planes, it acts at 90° to the surface.
• Weight (gravitational force) always acts straight downward.
• Tension is a force in a rope or cord pulling on a body, always directed away from the body.
• Friction opposes the motion of two surfaces in contact; it acts opposite the direction of potential or actual motion.

Frictional Forces

• Frictional force formula: ( f = \mu N ), where μ is the coefficient of friction and N is normal force.
• Static friction resists motion before an object starts moving (v = 0).
• Kinetic friction exists when there is relative motion between surfaces: ( f_k = \mu_k N ).

Newton’s Laws of Motion

• Newton's First Law: An object remains at rest or in uniform motion unless acted on by a net force (static/dynamic equilibrium: total F = 0).
• Newton’s Second Law: The net force on an object is equal to mass times acceleration (( F_{\text{total}} = ma )).
• Newton’s Third Law: Every action has an equal and opposite reaction.

Free Body Diagrams and Equations

• Free body diagrams show all forces on an object; arrows start from the dot (object) and indicate direction.
• For forces at angles, resolve each into x (horizontal) and y (vertical) components using trigonometry.
• The sum of forces in the x and y directions equals ( ma_x ) and ( ma_y ), respectively.

Example Problems

• For objects on inclined planes, define axes parallel (x) and perpendicular (y) to the surface.
• Decompose weights into x (( mg \sin \theta )) and y (( mg \cos \theta )) components.
• When moving at constant speed, acceleration ( a = 0 ), so total forces in each direction sum to zero.
• In multi-object systems (e.g., pulley), set up separate force equations for each mass and solve simultaneously.

Key Terms & Definitions

• Normal Force — Perpendicular contact force exerted by a surface on an object.
• Tension — Pulling force transmitted by a rope or cord, directed away from the body.
• Friction (Static/Kinetic) — Force opposing motion; static is before movement, kinetic is during movement.
• Coefficient of Friction (μ) — Value describing the amount of friction between two surfaces.
• Free Body Diagram — Diagram showing all forces acting on a body.
• Equilibrium — State where total forces sum to zero; no acceleration.
• Inclined Plane — Surface set at an angle to the horizontal.

Action Items / Next Steps

• Practice drawing and labeling free body diagrams for various surfaces.
• Solve additional problems involving forces on inclined planes with friction.
• Review and memorize the formulas for friction, force components, and Newton’s laws.