Transcript EQUILIBRIUM OF PARTICLES

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

F  0
where

F
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 (

F
) 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


i and j
components. In this case the equation of equilibrium,

F

0



F  Fx i  Fy j  0
Fx  0
Fy  0
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,

F
  0


F  Fx i  Fy j  Fz k  0
Fx  0
Fy  0
Fz  0
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.
Free Body Diagram Samples
Vertically stacked blocks
Free Body Diagram
Forces on the blocks
A block on an incline with spring
Forces on block
Free Body Diagram
Strings joining at a point
A block and tackle system
FBD of pulley
Collar on rod
FBD of Collar
Ff