EQUILIBRIUM OF PARTICLES Only concurrent forces can act

EQUILIBRIUM OF PARTICLES

Only concurrent forces can act on a particle whose shape and dimensions are neglected and its whole mass is assumed to be concentrated at a single point, its mass center. Equilibrium can be thought of as an unchanging – stable condition. All the bodies that are at rest are in equilibrium. A particle acted upon by balanced forces is in equilibrium provided it is at rest if originally at rest or has a constant velocity (moving along a straight path with constant speed) if originally in motion.

To maintain equilibrium, it is necessary to satisfy Newton’s first law of motion, which requires the resultant force acting on a particle to be equal to zero. This condition may be stated mathematically as where is the vector sum of all the forces acting on the particle. This equation is not only a necessary condition for equilibrium; it is also a sufficient condition.

THE FREE BODY DIAGRAM (FBD) SERBEST CİSİM DİYAGRAMI (SCD) To apply the equation of equilibrium, we must account for all the known and unknown forces ( ) which act on the particle. The best way to do this is to draw the particle’s free body diagram (FBD). This diagram is simply a sketch which shows the particle “free” from its surroundings with all the forces that act on it.

Procedure for Drawing a Free Body Diagram: 1. Draw Outlined Shape: Imagine the particle to be isolated or cut “free” from its surroundings by drawing its outlined shape. A simplified but accurate drawing is sufficient. Particles will be drawn as unique points comprised of the mass center of the particle.

2. Set up the Reference System: If not indicated, set up a reference system in accordance with the geometry of the problem. 3. Indicate Forces: On the sketch, indicate all the forces that act on the particle. These forces can be 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.

4. Label Force Magnitudes: The forces that are known should be labeled with their proper magnitudes and directions. Letters are used to represent the magnitudes and directions of forces that are unknown. 5. Employ Equation of Equilibrium: Finally, equation of equilibrium must be employed to determine the desired quantities. Care must be given to the consistency of units used.

Coplanar Force Systems If a particle is subjected to a system of coplanar forces that lie in the x-y plane, then each force can be resolved into its and components. In this case the equation of equilibrium, Note that both the x and y components must be equal to zero separately. Since there are two scalar equations to be used at most two unknowns can be determined.

Three Dimensional Force Systems If a particle is under the effect of spatial forces then each force can be resolved into its x, y and z components. In this case, Since there are three scalar equations to be used at most three unknowns can be determined. In the three dimensional case, the forces must be represented in vector form.