Mechanical Engineering Principles

28 MECHANICAL ENGINEERING PRINCIPLES

3.5 Triangle of forces method

A simple procedure for the triangle of forces method
of vector addition is as follows:

(i) Draw a vector representing one of the forces,

using an appropriate scale and in the direction

of its line of action.

(ii) From thenoseof this vector and using the

same scale, draw a vector representing the

second force in the direction of its line of

action.

(iii) The resultant vector is represented in both
magnitude and direction by the vector drawn
from the tail of the first vector to the nose of
the second vector.

Problem 2. Determine the magnitude and

direction of the resultant of a force of 15 N

acting horizontally to the right and a force of

20 N, inclined at an angle of 60°to the 15 N

force. Use the triangle of forces method.

Using the procedure given above and with reference
to Figure 3.8:

(i) abis drawn 15 units long horizontally

0

35 °^60 °

c

ab

30.5 N

15 N

20 N

Scale

5 10 15 20 N (force)

Figure 3.8

(ii) Fromb,bcis drawn 20 units long, inclined

at an angle of 60°toab. (Note, in angular

measure, an angle of 60°fromabmeans 60°

in an anticlockwise direction)

(iii) By measurement, the resultantacis 30.5 units
long inclined at an angle of 35°toab.That
is, the resultant force is30.5 N, inclined at an
angle of 35 °to the 15 N force.

Problem 3. Find the magnitude and

direction of the two forces given, using the

triangle of forces method.

First force: 1.5 kN acting at an angle of 30°

Second force: 3.7 kN acting at an angle

of− 45 °

Scale

0

3.7 kN

4.3 kN

1234kN(force)

1.5 kN

a

b

c

30 °^45 °

25 °

Figure 3.9

From the above procedure and with reference to

Figure 3.9:

(i) abis drawn at an angle of 30°and 1.5 units

in length.

(ii) Fromb,bcis drawn at an angle of− 45 °and

3.7 units in length. (Note, an angle of− 45 °

means a clockwise rotation of 45°from a line

drawn horizontally to the right)

(iii) By measurement, the resultantacis 4.3 units

long at an angle of− 25 °. That is, the resultant

force is4.3 kNat an angle of− 25 °

Now try the following exercise

Exercise 12 Further problems on the tri-

angle of forces method

In questions 1 to 5, use the triangle of forces

method to determine the magnitude and direc-

tion of the resultant of the forces given.

1. 1.3 kN and 2.7 kN, having the same line
   of action and acting in the same direction.
   [4.0 kN in the direction of the forces]


2. 470 N and 538 N having the same line of
   action but acting in opposite directions.
   [68 N in the direction of the 538 N force]