Answer to Question #94900 in Mechanics | Relativity for Arra

Question

find the magnitude and direction of the resultant of a 10N-Force that acts angle 40 clockwise from the +x- axis, a 7-N force that acts an angle of 180 clockwise from the + y-axis, 5 -N force that acts at an angle 90 Clockwise from the +y-axis.

Answer 1

The resultant force

$${\bf R}=\bf F_1+F_2+F_3$$

Components of resultanf force

$$R_x =F_{1x}+F_{2x}+F_{3x}$$

$$=10\cos 40^{\circ}+0+5=12.66\:\rm N$$

$$R_y =F_{1y}+F_{2y}+F_{3y}$$

$$=-10\sin 40^{\circ}-7+0=-13.43\:\rm N$$

The magnitude of a resultant force

$$R=\sqrt{R_x^2+R_y^2}=\sqrt{(12.66)^2+(-13.43)^2}=18.5\:\rm N$$

The direction of a resultant force

$$\theta=\tan^{-1}\left(\frac{R_y}{R_x}\right)$$

$$=\tan^{-1}\left(\frac{-13.43}{12.66}\right)=46.7^{\circ}\quad ({\rm clockwise\;from\; the}\; +x\:\rm axis)$$