CH 3STATICS OF PARTICLES

System ofForces

Coplanar 2D

Concurrent Nonconcurrent

ParallelGeneral

Noncoplanar 3D

Nonconcurrent

Parallel General

Concurrent

Free-Body Diagrams

2 - 7

Free-Body Diagrams

Space Diagram: A sketch showing

the physical conditions of the

problem.

Free-Body Diagram: A sketch showing

only the forces on the selected particle.

2 - 8

Equilibrium of a Particle• When the resultant of all forces acting on a particle is zero, the particle is

in equilibrium.

• Particle acted upon by

two forces:

- equal magnitude

- same line of action

- opposite sense

• Particle acted upon by three or more forces:

- graphical solution yields a closed polygon

- algebraic solution

00

0

==

==

yx FF

FR

• Newton’s First Law: If the resultant force on a particle is zero, the particle will

remain at rest or will continue at constant speed in a straight line.

example

◼ The cable system shown in Fig. 3-8 is being

used to lift body A. The cable system is in

equilibrium at the cable positions shown in the

figure when a 500-N force is applied at joint 1.

Determine the tensions in cables A, B, C, and

D and the mass of a body A that is being lifted.

◼ 2.10 To steady a sign as it is being lowered, two cables are

attached to the sign at A. Using trigonometry and knowing that

the magnitude of P is 300 N, determine

a) The required angle if the responding R of the two forces

applied at A is to be vertical

b) The corresponding magnitude of R.

Solution (a)

Using the triangle rule and the law of sines

360 N

300 N

35˚

R

Solution (b)

β= ?We need to calculate the value of βto find the value

of R

Law of Sinus a/sin A = b/sin B = c/sin C

R = 513 N

360 N

300 N

35˚

R

Equilibrium of Forces

F4 = 400 N

F3 = 200 N

F2 = 173.2 F1 = 300

O

OF1 = 300

F2 = 173.2 N F3 = 200

F4 = 400 N

30

30

An equilibrium system of forces

produces a closed force polygon

Example Figure .27 shows four forces acting on A.In figure .28, the resultant of the given forcesis determined by the polygon rule. Starting from point O with F1 and arranging the forces in tip-to-tail fashion,we find that the tip of F4 coincides with thestarting point O. Thus the resultant R of the given system of forces is zero, and the particle is in equilibrium.

The closed polygon drawn in Fig 2.28 provides a graphical expression of the equilibrium of A.To express algebraically the condition for the equilibrium of a particle, we write

Resolving each force F into rectangular components,we have

We conclude that the necessary and sufficientconditions for the equilibrium of a particle are

Returning to the particle shown in figure 2.27, we check that the equilibrium conditions are satisfied. We write