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?

 

[baba89]

I would approach this problem by first considering the forces acting on the ring and the string. In the first scenario, the only forces acting on the ring are its weight w and the tension in the string. Since the ring is in equilibrium, the sum of these forces must be equal to zero. Therefore, we can set up the following equation:

T - w = 0

Where T is the tension in the string. Solving for T, we get T = w. This means that the tension in the string is equal to the weight of the ring.

In the second scenario, an additional horizontal force of magnitude w is applied to the ring. This means that the sum of the forces acting on the ring is now equal to w + T. Since the ring is still in equilibrium, this sum must still be equal to zero. Therefore, we can set up the following equation:

w + T = 0

Substituting T = w (from the previous scenario), we get:

w + w = 0

Solving for w, we get w = 0. This means that the tension in the string is zero when the horizontal force is applied to the ring.

In conclusion, the tension in the string is equal to the weight of the ring in the first scenario, and it becomes zero when an additional horizontal force is applied to the ring in the second scenario. This is because the horizontal force cancels out the tension in the string, resulting in a net force of zero and equilibrium.