Question

A light string has its ends tied to two walls
separated by a distance equal to three-fourths
the length of the string as shown in the figure.
An 11 kg mass is suspended from the center
of the string, applying a tension in the string.
http://i1323.photobucket.com/albums/u599/sodone1/Untitled_zpsc34d60b3.png
What is the tension in the two strings of
length
L
2
tied to the wall? The acceleration of
gravity is 9.8 m/s2
.
Answer in units of N

Answer 1

Let tension in the left string be T1 and that in the right string be T2
(from symmetry the values of T1 and T2 would be equal and the problem can be solved faster. Just let me know if you need a clarification on this)

So T1 = T2 = T (say)

Net downward force on the block = mg
and net upward force = \[Tsin \theta + Tsin \theta = 2Tsin \theta \]

From the figure,
\[\cos \theta = \frac{ 3 }{ 8 } / \frac{ 1 }{ 2 } = \frac{ 3 }{ 4 } \]

\[Therefore, \sin \theta = \sqrt{7} / 64 \]

since the block is not moving, the net upward force must be equal to net downward force.

Therefor,

\[2Tsin \theta = mg \]

2*T* \[2*T* \sqrt{7} / 64 = 11 * 9.8 \]

You can calculate T from this expression.
Since we have consistently used S.I. units,
the answer for T would automatically be in its S.I. unit, which is N

Answer 2

ok i got that t= 1303.83 but my quest said that's not correct