Mechanical Engineering Principles

32 MECHANICAL ENGINEERING PRINCIPLES

70 N

60 N

80 N

80 °

30 °

60 °

Figure 3.17

60 N

80 N

70 N

30 °

a

b

c

0

Scale 0 20 40 60 N

φ

Figure 3.18

The vector diagram is shown in Figure 3.18,oa
representing the 60 N force,ab representing the
80 N force andbcthe 70 N force. The resultant,
oc, is found by measurement to represent a force of
112 N and angleφis 25°.
Thus, the five forces shown in Figure 3.16 may
be represented by a single force of 112 N at 25°
to the horizontal.

Now try the following exercise

Exercise 15 Further problems on the re-

sultant of more than two cop-

lanar forces

In questions 1 to 3, determine graphically the

magnitude and direction of the resultant of the

coplanar forces given which are acting at a

point.

1. ForceA, 12 N acting horizontally to the
   right, forceB, 20 N acting at 140° to
   forceA,forceC, 16 N acting 290° to
   forceA. [3.06 N at− 45 °to forceA]
   2. Force 1, 23 kN acting at 80°to the hor-
   izontal, force 2, 30 kN acting at 37° to
   force 1, force 3, 15 kN acting at 70°to
   force 2.
   [53.5 kN at 37°to force 1
   (i.e. 117°to the horizontal)]
   3. ForceP, 50 kN acting horizontally to the
   right, forceQ,20kNat70°to forceP,
   forceR, 40 kN at 170°to forceP, force
   S, 80 kN at 300°to forceP.

[72 kN at− 37 °to forceP]

4. Four horizontal wires are attached to a
   telephone pole and exert tensions of 30 N
   to the south, 20 N to the east, 50 N to
   the north-east and 40 N to the north-west.
   Determine the resultant force on the pole
   and its direction.

[43.18 N at 38.82°east of north]

3.9 Coplanar forces in equilibrium

When three or more coplanar forces are acting at

a point and the vector diagram closes, there is

no resultant. The forces acting at the point are in

equilibrium.

Problem 8. A load of 200 N is lifted by

two ropes connected to the same point on the

load, making angles of 40°and 35°with the

vertical. Determine graphically the tensions

in each rope when the system is in

equilibrium.

F 2 F 1

35 ° 40 °

200 N

Figure 3.19