Equilibrium: The figure shows two forces acting at right angles on an object. They have magnitudes = 6.3 N and = 2.1 N. What third force will cause the object to be in equilibrium (acceleration equals zero)? A) 6.6 N at 162° counterclockwise from ₁ B) 6.6 N at 108° counterclockwise from ₁ C) 4.2 N at 162° counterclockwise from ₁ D) 4.2 N at 108° counterclockwise from ₁

Question

Quizplus · Accepted Answer

For the object to be in equilibrium, the third force must be equal in magnitude and opposite in direction to the resultant of the two given forces. Using vector addition, the resultant force has a magnitude of sqrt((6.3^2) + (2.1^2)) = 6.6 N and is at an angle of arctan(2.1/6.3) = 18° counterclockwise from the horizontal (or 162° counterclockwise from the vertical). Therefore, the third force must have a magnitude of 6.6 N and be at an angle of 162° counterclockwise from the vertical (or 18° clockwise from the horizontal). The only choice that matches this description is A.

Equilibrium: the Figure Shows Two Forces Acting at Right Angles