Relationship between belt tension and pressure it exerts

  • Thread starter Oseania
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  • #1
Oseania
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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.


Wire_tension_pressure.png
 

Answers and Replies

  • #2
ergospherical
883
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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##.
 

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