Two forces, each of 10 N, act at a point P as shown in the diagram. The angle between the directions of the forces is 120°.

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Question 16

Two forces, each of 10 N, act at a point P as shown in the diagram. The angle between the directions of the forces is 120°.

What is the magnitude of the resultant force?

A 5N                B 10N              C 17N              D 20N

Reference: Past Exam Paper – June 2003 Paper 1 Q3

Solution:

Answer: B. 

Since the angle on the right of the diagonal vector is 120° with the horizontal, the angle on the LEFT of the diagonal vector is 180° – 120° = 60°with the horizontal.

Consider the resultant vector.

Since the 2 vectors given are of the same magnitude, we can assume that the triangle formed when the resultant is formed will at least be an isosceles triangle – that is, the angle that these 2 vectors make with the resultant vector will have the same value. Let this angle be x.

Sum of angles in a triangle is 180°.

60° + x + x = 180°

Angle x = (180° – 60°) / 2 = 60°

Since all the angles are equal in the triangle, it is actually an equilateral triangle. So, the sides will have the same magnitude.

Thus, resultant vector = 10N

The question can also be tackled using sine or cosine rule (depending on the values available).