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

0F

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.

F

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.

F

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,

0F

0

0

0

y

x

yx

F

F

jFiFF

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.

i

j

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,

0F

0

0

0

0

z

y

x

zyx

F

F

F

kFjFiFF

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

Free Body Diagram

Vertically stacked blocks

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

Ff

Collar on rodFBD of Collar