The figure shows two forces acting at right angles on an object.They have magnitudes F₁ = 6.3 N and F₂ = 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

Since the two given forces act at right angles, we can use the Pythagorean theorem to find the resultant force:

F = sqrt[(6.3 N)^2 + (2.1 N)^2] 
F = 6.6 N

To maintain equilibrium, the third force must be equal in magnitude but opposite in direction to the resultant force, so it must also be 6.6 N.

To find the direction, we use trigonometry. The angle between the horizontal and the resultant force can be found as:

theta = arctan(2.1 N / 6.3 N) 
theta = 18.4 degrees

Since the third force must be perpendicular to the resultant force, its angle with the horizontal will be:

90 degrees - 18.4 degrees = 71.6 degrees

However, the question asks for the angle counterclockwise from the first force, which is at an angle of -90 degrees (or 270 degrees) from the horizontal. Therefore, we add 270 degrees to 71.6 degrees to get:

theta = 342.6 degrees

To simplify this answer, we subtract 360 degrees to get an equivalent angle between 0 and 360 degrees:

theta = 342.6 degrees - 360 degrees = -17.4 degrees

Finally, we add 180 degrees to get the counterclockwise angle from the first force:

theta = -17.4 degrees + 180 degrees = 162.6 degrees

Therefore, the answer is A) 6.6 N at 162° counterclockwise from the first force.

The Figure Shows Two Forces Acting at Right Angles on an Object.They