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Dry Friction and Coulomb's Law

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Equilibrium of Rigid BodiesAnalysis of Frames and Machines+1 more→→Belt and Rope FrictionFriction Applications: Wedges, Screws, and Belts+2 more
statics friction Coulomb friction static friction kinetic friction

Core Idea

Coulomb's law states that the maximum static friction force is F_s,max = μ_s·N, where μ_s is the static friction coefficient and N is the normal contact force. Kinetic friction is F_k = μ_k·N with μ_k < μ_s. Friction is reactive: it takes whatever value is needed for equilibrium up to its maximum. Three states are possible — static equilibrium (F < μ_s·N), impending motion (F = μ_s·N), or sliding (F = μ_k·N). The angle of friction φ_s = arctan(μ_s) gives the angle of the resultant contact force from the normal at impending slip.

How It's Best Learned

Identify which friction state applies (equilibrium, impending, or sliding) before setting up equations. Assume a friction direction in the FBD, solve, and verify the result is consistent with the assumed state.

Common Misconceptions

Explainer

From your study of rigid-body equilibrium, you know how to sum forces and moments to find unknown reactions. Friction introduces something new: a contact force whose magnitude is not independently determined by geometry or applied loads, but instead adjusts to maintain equilibrium — up to a limit. This reactive character is what makes friction problems require a judgment call before you can write equations.

Coulomb's model describes the frictional contact between two dry surfaces with just two parameters: the static friction coefficient μ_s and the kinetic friction coefficient μ_k. The normal force N at the contact surface (perpendicular to the interface) is determined from equilibrium, exactly as in your earlier work. The friction force F acts tangentially and opposes the tendency of relative motion between the surfaces. The key rule: friction takes whatever value is needed for equilibrium, from zero up to its maximum F_s,max = μ_s·N. Only when the applied force would require F to exceed that maximum does sliding occur.

This gives three mutually exclusive states. In static equilibrium, the object is not on the verge of moving, and F < μ_s·N — you solve for F from the equilibrium equations. At impending motion, the object is on the verge of sliding, and F = μ_s·N — this is the tipping point condition used in most engineering problems about "will this object slide?" Once the object is actually sliding, the friction force drops to the kinetic value F_k = μ_k·N, with μ_k < μ_s (kinetic friction is always smaller than the maximum static value). The reduction in friction after motion begins is why it's easier to keep an object sliding than to start it sliding.

The angle of friction φ_s = arctan(μ_s) offers a geometric way to see the same physics. The total contact force on a surface has a normal component N and a tangential component F. The resultant of these two components makes an angle arctan(F/N) with the normal. At impending slip, this resultant sits exactly at angle φ_s from the normal — the friction cone. Any resultant direction inside the cone is achievable by static friction; outside the cone, the surface cannot provide the needed reaction and the object slides. This geometric view is especially powerful when analyzing wedges and screws, where the same friction angle appears in the inclined-plane geometry.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Center of Mass → Conservation of Linear Momentum → Elastic Collisions → Inelastic Collisions → Coefficient of Restitution → Collision Analysis and Real-World Applications → Two-Body Collisions in the Center-of-Mass Frame → Reduced Mass and Two-Body Problems → Kinematics in Two Dimensions → Projectile Motion → Circular Motion: Kinematics → Rotational Kinematics → Torque → Moment of Inertia → Rotational Kinetic Energy → The Work-Energy Theorem → Conservation of Mechanical Energy → Work-Energy Principle for Particles → Linear Impulse-Momentum for Particles → Linear Momentum and Impulse in Systems → Conservation of Linear Momentum in Systems → Systems of Particles: Center of Mass and Internal Forces → Rigid Body Kinetics — Force and Acceleration → Angular Impulse and Momentum for Rigid Bodies → Conservation of Angular Momentum → Euler's Equations for Rigid Body Rotation → Gyroscopic Motion, Precession, and Stability → Stability of Equilibrium: Stable, Unstable, and Neutral → Introduction to Statics and Dynamics → Vector Analysis and Components → Scalar and Vector Mechanics → Force Vectors, Components, and Resultants → Particle Equilibrium Conditions → Rigid Body Equilibrium: Planar Analysis → Statically Determinate Systems Analysis → Statically Determinate vs. Indeterminate Structures → Truss Analysis: Method of Joints → Truss Analysis: Method of Sections → Analysis of Frames and Machines → Dry Friction and Coulomb's Law

Longest path: 130 steps · 740 total prerequisite topics

Prerequisites (3)

Leads To (4)