N1 Engineering Science|The Easy Way! 23

2.1.6 Equilibrium D

Definition 2.6 Equilibrium When a system of forces acts on a point and it remains at rest, the forces are in equilibrium.

2.1.7 Equilibrant D

Definition 2.7 Equilibrant Equilibrant is that single force which brings equilibrium to a system of forces.

Te equilibrant is equal in magnitude but opposite in direction to the resultant.

In section 1.4.2, page 7, it was seen how the series or sequence method of addition of vectors can be applied. Following is the parallelogram method.

2.2 Parallelogram of forces D

Te magnitude and direction of the resultant and equilibrant of two forces acting at a point can be determined graphically by making use of a parallelogram. Both forces must either push towards or pull away from the point of application.

Definition 2.8 Parallelogram of forces If two similar forces(i.e. two pulling or two pushing forces) acting on a point are represented as vectors by two adjacent sides of a parallelogram, their resultant will be represented in magnitude and direction by the diagonal of the parallelogram drawn from that point.

Example 2.2

Find the magnitude and direction of the resultant and equilibrant of the two pulling forces shown in fig. 2.1.

Method

• Select a suitable scale (100mm= largest force). • Sketching a shape or planning diagram will help with the positioning and to ensure that there is enough space to complete the parallelogram.

• Draw the vector diagrams of the forces. • Complete the parallelogramwith dotted lines.

35° 750 N Fig. 2.1 g. 2.1 650 N

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