Two known forces F1 = 3.55 N at 74.0° below the positive x-axis and F2 = 2.80 N at 32.0° below the negative x-axis are acting on an object. What is the magnitude of the third force F3 so that the acceleration of the object is zero?

5.09N

Explanation:

The force required is the equilibrant force. This is defined as that force in a given force system that brings about balance in the system. It is equal in magnitude to the resultant force but opposite in direction to it.

Hence if we find the magnitude of the resultant force, we have already obtained the magnitude of the equilibrant force.

When the forces of a system are balanced, the resultant acceleration is zero.

Given;

The angle between the forces is deduced to be ( see the diagram below).

Applying the parallelogram law of vectors, the resultant force F is thus given as follows;

therefore;

See the diagram below;

The green line represents the equilibrant force needed to bring about a balance to make the body have a zero acceleration.  It is equal in magnitude but opposite in direction to the resultant F.