How Do You Calculate the Tension in a String With Hanging Mass and Pulleys?

[mirandasatterley]

Homework Statement

A 12 kg object hangs in equilibrium from a string with a total length of L=5m and a linear mass density of u= 0.001kg/m. The string is wrapped around two light, frictionless pulleys that are separated by a distance of d=2m. Determine the tension in the string.

Sorry i don't have a picture but - the pulleys are at the top an the rope goes around them with a hanging mass, forming an inverted triangle.

Homework Equations

The Attempt at a Solution

Normally, i would write equation for the sum of the forces on the x and y axis:

If there was an axis at the bottom of the inverted triangle and the angles were measured from the axis to the strings;

sum of forces on x-axis = T(right) cos theta - T(left) cos theta = 0
sum of forces on y-axis = mg - T(right)sin theta - T(left)sin theta = 0,
But since i don't know the angles, this goes nowhere.

I have also tried using;
v = Square root of (tension/u), but I don't have v,
So i tried to find v using f = v/ wavelength, but i don't have frequency.

I have tried so many things and I can't seem to get a start. Any hints?

 

[andrevdh]

If one ignores the mass of the string the tension in it is simply the weight of the 12 kg object. This one can deduce from the fact that the tension in the string needs to balance the weight of the object in order to keep it in equilibrium.