The greatest and least resultant of two forces acting at a point are 1

1.	The greatest and least resultant of two forces acting at a point are 17N and 7N respectively. Find the two forces. If these forces act at right angles, find the magnitude of their resultant.
Answer» For maximum resultant P + Q=17N ........... (1) For minimum resultant P - Q = 7N .............. (2) Eq(1) + (2) gives 2P = 24 Or P = \(\frac {24}{2}\) = 12N. From (1), Q = 17 - 12 = 5N When P and Q are in perpendicular directions, R = \(\sqrt {P^2+O^2}\) = \(\sqrt {12^5+5^2}\) = 13N (∵ cos 90° = 0).

The greatest and least resultant of two forces acting at a point are 17N and 7N respectively. Find the two forces. If these forces act at right angles, find the magnitude of their resultant.

Answer»

For maximum resultant

P + Q=17N ........... (1)

For minimum resultant

P - Q = 7N .............. (2)

Eq(1) + (2) gives 2P = 24 Or P = \(\frac {24}{2}\) = 12N.

From (1), Q = 17 - 12 = 5N

When P and Q are in perpendicular directions,

R = \(\sqrt {P^2+O^2}\)

= \(\sqrt {12^5+5^2}\)

= 13N

(∵ cos 90° = 0).