Chap3. Equilibrium of Force

Objectives

  • To introduce the concept of the free-body diagram for a particle
  • To show how to solve particle equilibrium problems using the equation of equilibrium

3.1 Condition for the Equilibrium of a Particle

(1) equilibrium : if it remains at rest if originally at rest(static equilibrium), or has a constant velocity if originally in motion \(\sum F = ma = 0​\) -> No acceleration

3.2 The Free-Body Diagram

(1) Procedure for Drawing a Free-doby Diagram

  • Draw Outlined Shape : Imagin the particle to be isolated or cut "free" from its surroundings
  • Show All Forces : Indicate on this sketch all the forces that act on the particle. These forces can be an active forces, which tend to set the particle in motion, or they can be reactive forces which are the result of the constraints or supports that tend to prevent motion. It may be helpful to trace around the particle's boundary, carefully noting each force acting on it
  • Identify Each Force : The forces that are known should be labeled with their proper magnitudes and directions

(2) Springs : if a linearly elastic spring of undeformed length is used to support a particle, the length of the spring will change in direct proportion to the force acting on it. A characteristic that defines the elasticity of a spring is the spring constant or stiffness k. \(F = kδ\)

(3) Cables and Pulleys

  • Cable can support only a tension or "pulling" force, this force always acts in the direction of the cable

3.3 ~ 3.4 Coplanar Force Systems

  • a force vector can be disected following the plane axis. Since it is on the static equilibrium condition, the sum of each force following the axis is zero. Negative sign describes the opposite direction.