Solve.
-Two forces of 40 and 120 N (newtons) act on an object. The angle between the forces is 22°. Find the magnitude of the resultant and the angle that it makes with the smaller force.
A) 158 N, 17°
B) 159 N, 17°
C) 157 N, 22°
D) 13 N, 17°

Question

Quizplus · Accepted Answer

The correct answer is A) 158 N, 17°.Explanation:The magnitude of the resultant force is given by:$$R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2\cos	heta}$$where F_1 and F_2 are the magnitudes of the two forces and θ is the angle between them.Substituting the given values, we get:$$R = \sqrt{40^2 + 120^2 + 2(40)(120)\cos22°} = 158 N$$The angle that the resultant force makes with the smaller force is given by:$$	heta_R = 	an^{-1}\left(\frac{F_2\sin	heta}{F_1 + F_2\cos	heta}ight)$$Substituting the given values, we get:$$	heta_R = 	an^{-1}\left(\frac{120\sin22°}{40 + 120\cos22°}ight) = 17°$$

Solve. -Two Forces of 40 and 120 N (Newtons) Act on on an Object