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).
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