three forces act on a ring. The net force on the ring is zero. One force is at an angle of 30 degrees with a magnitude of 40 Newtons. A second force F acts at an angle theta . The tangent of the angle is tan theta = 3 / �ã 3 . If the third force is n3 Newtons, what is n3?
Well, if the net force on the ring is zero, then all the forces must cancel each other out. So, let's take a closer look at the forces.
We know that the first force is at an angle of 30 degrees with a magnitude of 40 Newtons. That means this force is pulling the ring in one direction.
The second force, F, is at an angle theta. And we're told that the tangent of the angle is 3/√3. Now, I don't want to get all mathy on you, but I can tell you that the tangent of an angle is equal to the opposite side divided by the adjacent side. So, if we have a right triangle here, the opposite side must be 3 and the adjacent side must be √3. That means the second force is pulling the ring in a different direction.
Since the net force is zero, these two forces must have equal magnitudes but opposite directions. So, if the first force is pulling with a magnitude of 40 Newtons, the second force must also have a magnitude of 40 Newtons.
Now, let's talk about the third force, n3 Newtons. Since the net force is zero, this force must also cancel out the other two forces. That means the third force must have a magnitude of 40 Newtons as well.
So, n3 Newtons is 40 Newtons! Ta-da!