# Really simple, system in equilibrium (weight and tension in light string)

• furor celtica
In summary, the problem involves a small ring of mass 0.1 kg on a light string with fixed points A and B, hanging in equilibrium with the string inclined at 40° to the horizontal. The goal is to prove that both parts of the string are inclined at 40° and find the tension in the string. The solution involves understanding that the tension is the same all along the string and that the horizontal and vertical forces acting on the ring must sum up to zero in equilibrium. A visual representation of the forces can aid in understanding the proof.
furor celtica

## Homework Statement

A small smooth ring R of mass 0.1 kg is threaded on a light string. The ends of the string are fastened to two fixed points A and B. The ring hangs in equilibrium with the part AR of the string inclined at 40° to the horizontal, as shown in the diagram. Show that the part RB of the string is also inclined at 40° to the horizontal and find the tension in the string.

## The Attempt at a Solution

I have no difficulties with the second question, namely finding the tension in the string, but although it seems obvious to me that RB should be inclined at 40° to the horizontal, I’m at a loss to prove why in the most coherent way possible. I would be grateful for an outline on how to prove this concisely and effectively. Cheers

#### Attachments

• diagram.png
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It is a single string and the ring slides along it till it reaches equilibrium. The tension is the same all along the string. When in equilibrium, both the horizontal and vertical components of the forces acting on the ring sum up to zero. What are the horizontal force components? (Draw the forces.)

ehild

thanks

## 1. What is a "Really simple, system in equilibrium (weight and tension in light string)"?

A "Really simple, system in equilibrium (weight and tension in light string)" is a physics concept that describes a scenario where a light string or rope is supporting a weight, and the forces acting on the string are balanced, resulting in a state of equilibrium.

## 2. How is equilibrium achieved in this system?

Equilibrium is achieved in this system when the forces acting on the light string are balanced. This means that the weight of the object hanging from the string is equal to the tension force exerted by the string, resulting in a net force of zero and a stable system.

## 3. What factors affect the tension in a light string in this system?

The tension in a light string in this system is affected by two main factors: the weight of the object hanging from the string and the angle at which the string is pulled. The greater the weight or the steeper the angle, the greater the tension in the string.

## 4. What happens if the weight on the string is too heavy?

If the weight on the string is too heavy, the tension in the string will increase and may eventually exceed the breaking point of the string. This will result in the string breaking and the system no longer being in equilibrium.

## 5. How is this concept applied in real-life situations?

This concept is applied in various real-life situations, such as in construction and engineering, where ropes and cables are used to support heavy objects. It is also used in rock climbing and other activities that involve ropes and harnesses to ensure safety and balance.

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