# Tension of a String attached to a string

1. Feb 16, 2010

### AxeluteZero

1. The problem statement, all variables and given/known data
In figure (a) shown below, a 0.600-kg block is suspended at the midpoint of a 1.25-m-long string. The ends of the string are attached to the ceiling at points separated by 1.00 m.

(a) What angle does the string make with the ceiling?
36.9° <--- I found this answer already, and it IS correct

(b) What is the tension in the string?
4.9 N <--- Also a correct answer

(c) The 0.600-kg block is removed and two 0.3-kg blocks are attached to the string such that the lengths of the three string segments are equal (see figure (b)). What is the tension in each segment of the string?

The image of the pictures (a) and (b) can be found here:
http://i311.photobucket.com/albums/kk465/AxeluteZero/4-p-049-alt.gif

2. Relevant equations

So far, I've used the Pythagorean Theorem, and this formula from 2 applications of Newton's 3rd law:

m*g = 2*T sin ($$\theta$$)

and I'm pretty sure I have the equation for the 2nd and 3rd pieces:

mg + mg = 2T sin (x)

T (middle) = T cos (x)

3. The attempt at a solution

I tried using the original angle, 36.9 degrees, as x, but as I thought, the angle doesn't work (since it presumably got bigger). I've tried slicing up picture "b" into different parts (similar to what I did in part a - it required me to split it into two parts to find the angle to the right triangle, but I have a square in the second one).

I don't think my equations are the problem (it's possible), I believe the angle I'm using is incorrect. Any pointers?

2. Feb 16, 2010

### tramar

There's probably a few ways to go about this, but here's how I did it:

1) Instead of having equations for the tension in each piece of string, I made equations for the two points where the masses are hanging. For each point, I had equations for both the x and y directions.

2) Using the geometry of the problem, I found theta, the angle that the two pieces attached to the ceiling make with the ceiling. Theta does indeed change and you can't use your earlier answer. This is because adding the extra block does indeed change the angle.

3) Once you've found theta, it should be easy to calculate the tension in each piece. (Hint: It should be evident that both pieces attached to the ceiling have the same tension, since the entire problem is symmetric and the masses are the same.)