Question

The resultant of two forces acting at 60° is √13 N. When the same forces act at 90° the resultant is√10 N. Find the magnitude of the two forces.

Answer 1

Let P and Q be the two forces. When the angle between them is 60°, resultant force is √13 N. Thus

P + Q + PQ = 13 ..........(1)

When the angle is 90° resultant force is

P₂+ Q₂ =10 ......... (2)

Substituting (2) in (1)

10 + P = 13

PQ = 3 ............(3)

(P + Q)² = P²+ Q² + 2PQ

= 10 + 2 × 3 = 16

P + Q = 4 ............ (4)

(P - Q)² = P² + Q² - 2PQ

= 10 - 6 = 4

P - Q = 2 ............. (5)

2P = 6; 2Q = 2

P = 3N and Q = 1N.