6) The sum of the magnitudes of two forces acting at a
point is 18 and the magnitude of their resultant is 12.
if the resultant is at 90 degree with the force of smaller magnitude
What are the magnitudes of forces?
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Answer:
Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.
As the resultant force makes 90
∘
with the smaller force P then Q forms the hypotenuse of the triangle.
Thus, it can be written as,
Q
2
−P
2
=R
2
Q
2
−P
2
=(12)
2
Q
2
−P
2
=144 (1)
The sum of magnitudes of two forces is given as,
P+Q=18
Q=18−P (2)
Substituting the value from equation (2) in equation (1), we get
(18−P)
2
−P
2
=144
P=5N
Substituting the value of P in equation (1), we get
Q=18−5
=13N
Thus, the magnitude of the forces are 5N and 13N.
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