Question

The sum of the magnitudes of two forces
acting at a point is 16N. The resultant of
these forces is perpendicular to the
smaller forces and has magnitude of 8 N.
If the smaller forces of magnitude x then
the value of x is​

Answer 1

Answer:

the two force vectors OA and OB make obtuse angle in between them and their resultant is perpendicular to OA

Let |OA| = x N ,   |OB| = (16-x) N  and resultant |OC| = 8N.  ΔOCA is right triangle and OACB is a parallelogram.

Hence  AC = OB .

we have |F1|2 + |R|2  = |F2|2  or x2 + 82 = (16-x)2 ..................(1)

solving (1) for x, we get x = 6 N . Hence forces are 10 N and 6 N