# Exploring Radial Forces Generated by Wrapping Strings

• I
• Safety Lab
In summary, the question is about the forces generated when pulling on both ends of a string wrapped around a finger. Assuming zero friction, the tension in the string is constant and there is a radial force expressed as force per unit length. By making a free body diagram and solving for the force, it is determined that the force is equal to the tension divided by the radius of the finger. This is similar to the equations for hoop stress in a thin walled pressure vessel.

#### Safety Lab

Hello all,

I have been racking my brain with this one all day and I can't seem to figure it out. I have been looking into the forces that would arise from wrapping a string, wire, etc. around your finger. The scenario is illustrated in the attachment. Basically the question is, if we start to pull on both ends of the string with some force, F, eventually the loop will tighten around the finger. I am curious, what kind of radial force would be generated here? If we assume that the finger is not compressible, then a greater and greater force will build the more force we apply at the ends, right? I am basically looking for an equation that would translate a horizontal forces on the ends throughout the loop. I understand that will probably relating the force applied and the angle of loop and what not. If it is a FEM type of question, fine, I just want to figure it out.

THANKS!

#### Attachments

• Finger_lig.png
6.9 KB · Views: 380
Start by assuming zero friction between the string and the finger. Then the tension in the string is constant along the entire length of the string. Call that tension T.

There is a radial force under the string. That force is expressed as force per unit length - typically pounds per inch or Newtons per meter. Call that force F.

Now make a free body diagram by slicing the finger down the middle so that the string is wrapped 180 degrees. Since this is a free body physics finger, no pain or blood is involved.

Then 2T = F X 2r, where r is the radius of the finger. Solve for F, and F = T / r. It's very similar to the equations for hoop stress in a thin walled pressure vessel.

## 1. What are radial forces?

Radial forces are forces that act along a straight line from a center point. In the context of wrapping strings, they refer to the forces generated when a string is wrapped around an object or surface.

## 2. How are radial forces generated by wrapping strings?

Radial forces are generated by the tension in the string as it is wrapped around an object. As the string is pulled taut, it exerts a force on the object or surface it is wrapped around.

## 3. Why is exploring radial forces generated by wrapping strings important?

Understanding radial forces can have practical applications in various fields such as engineering, physics, and biology. It can help in designing structures, predicting the behavior of materials, and studying the mechanics of biological systems.

## 4. What factors affect the magnitude of radial forces?

The magnitude of radial forces depends on several factors such as the tension in the string, the angle at which it is wrapped, the properties of the object or surface it is wrapped around, and the friction between the string and the object.

## 5. How can we measure radial forces generated by wrapping strings?

There are various methods for measuring radial forces, including using force sensors, strain gauges, and mathematical models. Experimentation and data analysis are also crucial in accurately measuring and understanding these forces.