Question

two forces act at 60 degrees and their resultant is 14 neutons, if they act at 90 degrees their resultant is 90 degrees. find the mangitude of forces?

Answer 1

A2A.

Let the magnitude of the two forces be x and y.

Let resultant at right angle be p(= √15N) and at 60 degrees be q(= √18N.

Now, p = √(x2 + y2) = √15,

q = √(x2 + y2 +2xycos60) = √18.

So x2 + y2 = 15,

x2 + y2 + xy = 18,

therefore xy = 3 or y = 3/x.

Now, x2 + (3/x)2 = 15,

x4 + 9 = 15x2,

x4 - 15x2 + 9 = 0.

Now find the roots of this quadratic equation, the two values of x will correspond to the magnitudes of the two vectors.