Tricky Conceptual Question Regarding Mass Rotating Horizontally from StringHELP

[spikey151]

Homework Statement

Okay, so this is more of a conceptual question. Imagine there is a point mass of mass "m" at the end of a string and the other end of the string is secured.

At first, when the point mass and string is just hanging vertically with the mass at the bottom and the string secured at the top, the free body diagram of the mass would just be a force of gravity downward and a tension force upward, counteracting the gravity force right?

Then, consider that the mass begins swinging around in a circle horizontally so that the string is at an angle \theta from the horizontal. Now if you draw a free body diagram from a side-view, the tension force is acting diagonally and the force of gravity is still acting downward. If tension force = T, then:
\sumF_y = T*sin\theta - mg = 0 and
\sumF_x = T*cos\theta = F_centripetal

So here's my main question, if the mass is swinging around in a circle fast enough (in other words, if the tangential speed is large enough) then the string would become horizontal correct, also meaning angle \theta equals zero? (correct me if I'm wrong) Now when the free body diagram is drawn, there is a horizontal tension force and a vertical gravity force. The horizontal tension force provides the required centripetal force for circular motion of the mass, but now what force is counteracting the force of gravity? The sum of all the vertical forces, which should be zero because the mass does not fall or have any vertical acceleration, would only involve force of gravity.

Homework Equations

F_centripetal = m*v²/r

The Attempt at a Solution

I do have one theory, which I'm not very sure about: Is it technically or physically impossible for the string to be completely horizontal? It only seems horizontal because the centripetal force (aka the horizontal component of the tension force) becomes so large that the gravitational force (aka the vertical component of the tension force) becomes negligible. But if this is the case, then when drawing the free-body diagram for the situation, is it physically incorrect if, along with the vertically downward force of gravity, a horizontal tension force is drawn acting on the mass?

Any help would be appreciated, I have the AP physics C mechanics test tomorrow -,-.

 

[spikey151]

Does nobody have any idea?? T_T

 

[Mapes]

Yes, it's physically impossible for the string to be horizontal in this scenario. You can draw a horizontal tension component, but the tension force also has a vertical component.