# Relationship between belt tension and pressure it exerts

• Oseania
In summary, the conversation discussed the relationship between the pulling force and exerted pressure on an elastic object when a non-elastic belt is wrapped around it. It was found that for equilibrium, the tension force is equal to the product of the force per unit length and the radius.

#### Oseania

TL;DR Summary
If I wrap a belt around my waist and pull, what is the relationship between the pulling force and exerted pressure to my waist?
I have following setup where a non-elastic belt is wrapped around an elastic object, like leather belt around waist. When I pull the belt with force F, it tightens around the elastic object and the belt exerts force to the elastic object. I would like to know what is the relationship between the pulling force F and the exerted pressure (or force) to the elastic object.

Take a small element of arc which subtends an angle of ##2\theta##. If the force per unit length is denoted ##p##, and the radius ##r##, then the net force on the element in the radial direction is\begin{align*}
F = 2\theta r p - 2T\sin{\theta} \sim 2\theta r p - 2T \theta
\end{align*}For equilibrium, ##T = rp##.

## 1. What is the relationship between belt tension and pressure it exerts?

The relationship between belt tension and pressure it exerts is directly proportional. This means that as belt tension increases, the pressure it exerts on the objects it is in contact with also increases.

## 2. How does belt tension affect the pressure it exerts?

Belt tension affects the pressure it exerts by pulling the belt tighter, which increases the force applied to the objects it is in contact with. This results in a higher pressure being exerted on the objects.

## 3. What factors can affect the relationship between belt tension and pressure it exerts?

The relationship between belt tension and pressure it exerts can be affected by factors such as the type and material of the belt, the speed at which it is moving, and the surface and material of the objects it is in contact with.

## 4. How does the angle of contact between the belt and objects affect the relationship between belt tension and pressure it exerts?

The angle of contact between the belt and objects can affect the relationship between belt tension and pressure it exerts by changing the direction of the force applied. As the angle of contact increases, the force applied in the direction of the objects decreases, resulting in a decrease in pressure exerted.

## 5. Why is understanding the relationship between belt tension and pressure it exerts important?

Understanding the relationship between belt tension and pressure it exerts is important in various industries such as manufacturing, transportation, and agriculture. It allows for the proper selection and maintenance of belts to ensure optimal performance and safety. It also helps in predicting and preventing potential failures or damage to equipment and objects in contact with the belt.