Tension in objects in circular motion

[nopeudon]

Homework Statement

Acrobat-dude swings two cups of liquid which are attached to ends of a string. He swings the two cups by holding onto the middle of the string. The acrobat then releases his hold on the string and the question asks what is the tension in the string at this point. The answer and working provided is simply as follows:

T = mv^2/r, then proceeds to substitute values provided in question. Magnitude of velocity used is the minimum value needed for liquid at top cup to stay in cup.

Can someone elaborate on how this works?

Homework Equations

summation F = mv^2/r

The Attempt at a Solution

So, obviously the source of centripetal acceleration initially is the tension in the string. When the cups are directly above each other, the tensions pulling on the two cups are different, because:

summation of forces for both cups = mv^2/r = T - W for bottom cup but T + W for top cup => T is smaller for top cup.

After the hold is released, T in the string becomes a single value. I'm confused as to how to proceed.

 

[Maharshi Roy]

Please specify whether the motion is in vertical frame or horizontal?

 

[nopeudon]

Oh, forgot to mention- motion is in vertical frame, hence my references to top/bottom cup, as well as why tensions in the rope was different before hold was released.