Question

two forces of 5n and 10n are acting at an inclination of 120 between them . find the magnitude and direction of the resultant force​

Answer 1

Answer:

R^2= P^2+Q^2+2.P.Q.cos x.

R^2= (5 N)^2+(10 N)^2+2×5 N×10 N ×cos 120°.

R^2 = 25 N^2+100 N^2+ 2×5 N× 10 N×(-1/2).

R^2 = 125 N^2 - 50 N^2.

R^2 = 75 N^2.

R. = 5√3 N. = 5×1.732 N. = 8.66 N.

Direction of resultant:-

tan(theta) = (Q.sin x)/(P+Q.cos x).

theta = tan^-1 (5.sin 120°)/(10 - 5×1/2).

=tan^-1(5√3/2)/(15/2).

= tan^-1( 1/√3).

=30°.

Thus , the resultant is 8.66 N. making an angle of 30° with 10 N force. Answer.