Solve.
-Two forces of 330 and 250 N (newtons) act on an object. The angle between the forces is 15°. Find the magnitude of the resultant and the angle that it makes with the larger force.
A) 4 N, 6°
B) 574 N, 6°
C) 576 N, 6°
D) 575 N, 6°

Question

Quizplus · Accepted Answer

The magnitude of the resultant force can be found using the law of cosines: $R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2\cos(\theta)}$, where $F_1$ and $F_2$ are the magnitudes of the two forces and $\theta$ is the angle between them. Substituting the given values, $R = \sqrt{330^2 + 250^2 + 2(330)(250)\cos(15^\circ)}$, which approximately equals 575 N. The angle $\phi$ that the resultant makes with the larger force can be found using the law of sines: $\frac{\sin(\phi)}{F_2} = \frac{\sin(\theta)}{R}$. Solving for $\phi$ gives an angle close to 6°.

Solve. -Two Forces of 330 and 250 N (Newtons) Act on on an Object