Mechanical Engineering Principles

26 MECHANICAL ENGINEERING PRINCIPLES

original position. Thus a ball bearing in a

hemispherical cup is in stable equilibrium, as

shown in Figure 3.2(a).

(a)

Stable

equilibrium

(c)

Neutral

equilibrium

(b)

Unstable

equilibrium

Figure 3.2

(ii) An object is in unstable equilibrium if,

when a disturbing force is applied, the cen-

tre of gravity is lowered and the object moves

away from its original position. Thus, a ball

bearing balanced on top of a hemispherical

cup is in unstable equilibrium, as shown in

Figure 3.2(b).

(iii) When an object inneutral equilibriumhas
a disturbing force applied, the centre of grav-
ity remains at the same height and the object
does not move when the disturbing force is
removed. Thus, a ball bearing on a flat hor-
izontal surface is in neutral equilibrium, as
shown in Figure 3.2(c).

3.3 Forces

When forces are all acting in the same plane, they
are calledcoplanar. When forces act at the same
time and at the same point, they are calledconcur-
rent forces.
Force is avector quantityand thus has both a
magnitude and a direction. A vector can be repre-
sented graphically by a line drawn to scale in the
direction of the line of action of the force.
To distinguish between vector and scalar quanti-
ties, various ways are used.
These include:

(i) bold print,

(ii) two capital letters with an arrow above them

to denote the sense of direction, e.g.

−→

AB,

whereAis the starting point andBthe end

point of the vector,

(iii) a line over the top of letters, e.g.ABora

(iv) letters with an arrow above, e.g.−→a,

−→

A

(v) underlined letters, e.g.a

(vi) xi+yj, whereiandjare axes at right-angles

to each other; for example, 3i+ 4 jmeans 3

units in theidirection and 4 units in thej

direction, as shown in Figure 3.3

0123 i

1

2

3

4

j

A(3,4)

Figure 3.3

(vii) a column matrix

(

a

b

)

; for example, the vec-

torOAshown in Figure 3.3 could be repre-

sented by

(

3

4

)

Thus, in Figure 3.3,OA≡

−→

OA≡OA

≡ 3 i+ 4 j≡

(

3

4

)

The method adopted in this text is to denote vector

quantities inbold print. Thus,abin Figure 3.4 rep-

resents a force of 5 Newton’s acting in a direction

due east.

0

ab

W

N

S

5 N E

Scale

Tail Nose

Figure 3.4