Ch3 - 2 - 2D Forces - Equilibrium of a Particle, Free-Body Diagram & Coplanar Force Systems

Oct 29, 2026

Upload by hdkawk

Covers the equilibrium of a particle within a 2-D or coplanar force system, focusing on how to model forces using a free-body diagram (FBD). Explains the what, why, and how of drawing an FBD by isolating the particle and listing active and reactive forces with known values or variables. Derives 2-D equilibrium conditions using net force equal to zero and separates them into scalar equations for solving unknown cable tensions or angles. Includes worked applications and an example using an engine mass of 250 kg with computed TB and TD.

LanguageEnglish

CategoryExam

FormatPDF

Pages18

Reading Time45 min

AccessFree to download

Today’s Objectives

The What, Why and How of a Free Body Diagram (FBD)

Equations of 2-D Equilibrium

Example

Applications

Springs, Cables, and Pulleys

Spring Force and Tension Relation

Today’s Objectives EQUILIBRIUM OF A PARTICLE, THE FREE-BODY DIAGRAM & COPLANAR FORCE SYSTEMS : Students will be able to : a) Draw a free body diagram (FBD), and, b) Apply equations of equilibrium to solve a 2-D problem. APPLICATIONS For a spool of given weight, what are the forces in cablesAB and AC ? APPLICATIONS (continued) For a given cable strength, what is the maximum weight that can be lifted ? APPLICATIONS (continued) For a given weight of the lights, what are the forces in the cables? What size of cable must you use ? COPLANAR FORCE SYSTEMS (Section 3.3) This is an example of a 2-D or coplanar force system. If the whole assembly is in equilibrium, then particle A is also in equilibrium. To determine the tensions in the cables for a given weight of the engine, we need to learn how to draw a free body diagram and apply equations of equilibrium. you Why THE WHAT, WHY AND HOW OF A FREE BODY DIAGRAM (FBD) Free Body Diagrams are one of the most important things for to know how to draw and use. What ? -It is a drawing that shows all external forces acting on the particle. ? -It helps you write the equations of equilibrium used to solve for the unknowns (usually forces or angles) . How ? 1. Imagine the particle to be isolated or cut free from its surroundings. 2. Show all the forces that act on the particle. Active forces: They want to move the particle. Reactive forces: They tend to resist the motion. 3. Identify each force and show all known magnitudesand directions. Show all unknown magnitudes and / or directions as variables . A Note : Engine mass = 250 Kg FBD at A general, particle equilibrium Or, EQUATIONS OF 2-D EQUILIBRIUM A Since particle A is in equilibrium, the net force at A is zero. So FAB + FAC + FAD = 0 or 􀀶 F = 0 FBD atA In for a in , 􀀶 F = 0 or 􀀶Fx i + 􀀶Fy j = 0 = 0 i + 0 j (A vector equation) written in a scalar form,􀀶Fx = 0 and 􀀶 Fy = 0 These are two scalar equations of equilibrium (EofE) . They can be used to solve for up to two unknowns. EXAMPLE Note : Engine mass = 250 Kg FBD at A Write the scalar EofE: + 􀁯 􀀶 Fx = TB cos 30º – TD = 0 + 􀁮 􀀶Fy = TB sin 30º – 2.452 kN = 0 Solving the second equation gives: TB = 4.90 kN From the first equation, we get: TD = 4.25 kN SPRINGS, CABLES, AND PULLEYS Spring Force = spring constant * deformation, or F = k * S With africtionless pulley, T 1 = T2 .

FAQs

What is a free-body diagram (FBD) and what is it used for?

An FBD shows all external forces acting on a particle. It helps set up the equations of equilibrium to solve for unknown forces or angles.

How do you draw an FBD for a particle in a 2-D coplanar system?

Isolate (cut free) the particle, then draw all forces acting on it. Mark known magnitudes and directions and represent unknown magnitudes or directions as variables.

What are the equilibrium equations for a particle in 2-D?

At equilibrium, the net force at the particle is zero. This gives vector form FAB + FAC + FAD = 0, which becomes two scalar equations: ΣFx = 0 and ΣFy = 0.

How are cable tensions related when using a frictionless pulley?

With a frictionless pulley, the tension in the two cable segments is equal, so T1 = T2.

Oct 29, 2026

Upload by hdkawk