Solving String Tension for Weighted Rings

[kilianod]

Homework Statement

2.(i) A light inextensible string of length 5a is secured with its ends a horizontal distance 2a apart. A small smooth ring is free slide on the string and a weight w is attached to the ring. Determine the tension in the string.

(ii)A horizontal force of magnitude w is now applied to the ring. The system adjustes to become in equilibrium onc more. Determine he tension in the string.



2. The attempt at a solution
Ive tried this a few times, but it seems to get way too complicated. Any help would be appreciated!

 

[LowlyPion]

Homework Statement

2.(i) A light inextensible string of length 5a is secured with its ends a horizontal distance 2a apart. A small smooth ring is free slide on the string and a weight w is attached to the ring. Determine the tension in the string.

(ii)A horizontal force of magnitude w is now applied to the ring. The system adjustes to become in equilibrium onc more. Determine he tension in the string.



2. The attempt at a solution
Ive tried this a few times, but it seems to get way too complicated. Any help would be appreciated!

Maybe you could draw a diagram of what this ring would look like at equilibrium. Since nothing would be in motion wouldn't it simply be a matter of looking at the force vectors that would hold the ring in position?

Similarly for part 2. Just add in your extra force vector to the drawing and write the equations for X and Y forces yes?