Limiting Equilibrium

Introduction

Why are there two limiting equilibrium? Why does friction acts upwards? Why does friction acts downwards? Why is the object about to move up? Why is the object about to move down?

All these questions and concepts appear contradicting, but trust me, it’s easy once you get the hang of it.

Aim

This post is written with the assumption that you know the concept of forces and equilibrium. This post helps you to understand limiting equilibrium, but does not help you with calculations or problem solving.

Definition

Limiting equilibrium is the state a particle is in when it is on the point of sliding.

Example

It’s best to learn with example.

Imagine a small ring threaded on a rough rod which is fixed vertically. The ring is pulled upwards with a string at an angle, and the ring is in equilibrium.

Play around with the interactive flash below. Explanations are below the flash.

Interactive Flash
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Explanation

Initially, with a small force, the ring is about to slip downwards, and thus by definition, the ring is in limiting equilibrium. Frictional force tries to oppose this by acting upwards.

As you increase the force applied, there will be an instance when the vertical component of the force balances the downward force due to gravity. Frictional force does not act during this instance.

As force increases, the ring has the tendency to move upwards now. It wants to move upwards, but the friction acts downwards and stop the ring from moving. (Previously the ring wants to move downwards due to gravity.)

As force increases, the ring will reach limiting equilibrium again, but this time, it is about to slip upwards.

Conclusion

  • Note that there are 2 limiting equilibrium in this example.
  • There is actually a range of force which when applied, will not cause the ring to move.

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