IMG_1594.HEIC

# Statics ## Chapter 3 Particle Equilibrium ### 3.1 Condition for the Equilibrium of a Particle A particle is said to be in equilibrium if 1. It is at rest, or 2. Moving with constant velocity. *Newton's First Law of Motion* states that if the resultant force acting on a particle is zero, the pa...

# Statics ## Chapter 3 Particle Equilibrium ### 3.1 Condition for the Equilibrium of a Particle A particle is said to be in equilibrium if 1. It is at rest, or 2. Moving with constant velocity. *Newton's First Law of Motion* states that if the resultant force acting on a particle is zero, the particle will remain in equilibrium. **Two-force Body** If only two forces are acting on a particle, equilibrium requires that they must be equal in magnitude, opposite in direction, and collinear. ### 3.2 The Free-Body Diagram To solve problems dealing with equilibrium, we must consider *all* the forces acting on the particle. *Free-Body Diagram:* A sketch showing the particle freed from its surroundings with *all* the forces acting on it. ### 3.3 Coplanar Systems For a particle in equilibrium, the sum of the forces in each direction must be zero. $\sum F_x = 0$ $\sum F_y = 0$ **Procedure for Drawing a Free-Body Diagram** 1. Decide which object to isolate. 2. Sketch the isolated object. 3. Indicate all the external forces acting on the object. These forces can be active forces or reactive forces. 4. Clearly label each force with its magnitude and direction. ### 3.4 Three Dimensional Force Systems For a particle in equilibrium in three dimensions, the sum of the forces in each direction must be zero. $\sum F_x = 0$ $\sum F_y = 0$ $\sum F_z = 0$ Or, in vector form, $\sum \vec{F} = 0$ $\sum (F_x \hat{\imath} + F_y \hat{\jmath} + F_z \hat{k}) = 0$ **Procedure for Solving 3-D Equilibrium Problems** 1. Draw a free-body diagram of the particle. 2. Establish a convenient coordinate system. 3. Resolve all forces into their x, y, and z components. 4. Apply the equilibrium equations. 5. Solve for the unknowns.