Question

Two forces (F1=10N, ϴ1=37° and F2=8N, ϴ2=330° act on a 5kg object. Find the magnitude and direction of acceleration produced by the two forces

Answer 1

The components of resultant force

$$F_x=F_1\cos\theta_1+F_2\cos\theta_2\\ =10\cos 37^{\circ}+8\cos 330^{\circ}=15\:\rm N$$

$$F_y=F_1\sin\theta_1+F_2\sin\theta_2\\ =10\sin 37^{\circ}+8\sin 330^{\circ}=2.0\:\rm N$$

The components of the acceleration

$$a_x=F_x/m=15/5=3.0\:\rm m/s^2$$

$$a_y=F_y/m=2.0/5=0.4\:\rm m/s^2$$

The magnitude of acceleration

$$a=\sqrt{a_x^2+a_y^2}=\sqrt{3.0^2+0.4^2}=3.02\:\rm m/s^2$$

Direction:

$$\theta=\tan^{-1}\frac{a_y}{a_x}=\tan^{-1}\frac{0.4}{3.0}=7.6^{\circ}$$