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Chapter 3 Equilibrium of a particle

Chapter 3 Equilibrium of a particle. 3-1 Condition for the Equilibrium of a particle 1. Equilibrium A particle is in equilibrium provided it is at rest if originally at rest and in motion if originally moving at constant velocity. F 2. F 1.

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Chapter 3 Equilibrium of a particle

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  1. Chapter 3 Equilibrium of a particle

  2. 3-1 Condition for the Equilibrium of a particle 1. Equilibrium A particle is in equilibrium provided it is at rest if originally at rest and in motion if originally moving at constant velocity. F2 F1 F3 2. Necessary & Sufficient condition Newton’s first law of motion. F = 0 Newton’s second law of motion F = ma = 0 a = 0 = d V / d t V = Constant

  3. 3-2 Free-Body Diagram • 1.Definition of FBD • A FBD is a sketch of the particle ,which shows the particle”free” • from its surroundings with all the forces that act on it. • 2.Connections F • (1) Spring k • Linear elastic spring. • Hooke’s Law: F=KS S K:spring constant or stiffness. • S:stretch of spring. • If S(+) => F pulls the spring • S(-) => F pushes the spring • (2) Cables & pulleys • a. Negligible Weight, cannot be stretched . T’ • b. Support only a tension or pulling force . T • c. constant tension throughout its length . T=T’

  4. Ta=W Example A B C Tb Tc W • FBD of the ring at A • 3.Forces • (1) Active Force • a. Force tends to set the particle in motion. • b. Forces caused by attached cables, weight, or magnetic and • electrostatic interaction. • (2) Reactive Force • Forces caused by the constraints or supports tending to prevent • motion .

  5. 3-3 Coplanar Fore Systems ( 2 D ) 1. Particle equilibrium F1 Fn F2 F3 F1 , F2, F3, …Fn Coplanar force in x y plane. Equations of Equilibrium F= 0 In Cartesian vector form F = Fx+ Fy = Fx i+ Fyj= 0 Scalar equilibrium equations Fx = 0 Fy = 0

  6. 2. Procedure for analysis (1) Draw Free-Body Diagram (a) Establish the x y axes (b) Label all forces (2) Apply equations of equilibrium (a) Fx = 0 Fy = 0 (b) Fs = k s if more than two unknowns exists and a spring involves.

  7. 3-4 Three-Dimensional Force Systems 1. Particle equilibrium in 3D Hence equation of equilibrium is F = 0 In Cartesian Vector form Fxi + Fyj + Fz = 0 So F3 Z F2 Y F4 F1 X Fx = 0 Fy = 0 Fz = 0 2. Analysis Procedures Same as sec. 3.3.

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