What is stability?

What does “STABILITY” mean? It refers to “equilibrium”. From wikipedia: "Equilibrium is a state in which a coordinate of a particle, rigid body, or dynamical system is conserved". From McGill University blog on Physics: "Equilibrium is a state of a system in which the variables which describe the system are not changing". ???

More simply, what is “EQUILIBRIUM"? We have equilibrium when everything is still, motionless, stationary, immobile, static. If an object does not move, it is STABLE. If it moves, even if you try to stop it, it is NOT STABLE.

Examples of EQUILUBRIUM? The ball does not move in all of these three cases, so it is “equilibrium". But...

Different types of “equilibrium" Stable equilibrium Unstable equilibrium Neutral equilibrium Esercizio......................matching

Basic Glossary stable = (equilibrio) stabile stable = stalla, scuderia, allevamento unstable [ansteibol] = (equilibrio) instabile instable = è sbagliato, non esiste neutral [niu:tral] = (equilibrio) indifferente neutral = neutrale (persona, Paese), neutro (sapone, colore), folle (marcia dell’auto disinserita).

Stable equilibrium From McGill blog: In a Stable equilibrium if a small perturbation away from equilibrium is applied, the system will return itself to the equilibrium state. In simple words: If I move the ball from its position and I leave it free to move, it goes back to its initial position.

Unstable equilibrium From McGill blog: In an unstable equilibrium if a small perturbation away from equilibrium is applied, the system will move farther away from its equilibrium state. In simple words: If I move the ball and I leave it free to move, it moves away from its starting position.

Neutral equilibrium In simple words: If I move the ball and I leave it free to move, it stays there without neither moving away, nor going back to its starting position.

How to check if a system (different from the ball in the bowl) is stable or not? Let’s see some examples.

How is this system?

How is this system?

How is this system?

How is this system?

Why are these systems stable, unstable or neutral?

Stable equilibrium Note the position of B (where reaction force is applied) and G (gravity center, where the weight force is applied).

Unstable equilibrium Note the position of B (where reaction force is applied) and G (gravity center, where the weight force is applied).

Neutral equilibrium Note the position of B (where reaction force is applied) and G (gravity center, where the weight force is applied).

And… what about ships???

Before talking of ships, another example: …is this object stable or not?

It is stable, of course, but what about the position of B and G?

In this special case, something new happens: …in this case B moves and...

now let’s go back to ships…

Let’s see what technical literature (Fraser University notes) says about ship’s equilibrium:

Let’s see what technical literature (Fraser University notes) says about ship’s equilibrium: off B G G B

… so all ships are unstable? G B

G = Gravity, or centre of Gravity, where the weight force is applied. Usually the following letters are used to name the point where the forces are applied: G = Gravity, or centre of Gravity, where the weight force is applied. B = centre of Buoyancy, where the hydrostatic (Archimedes) force is applied. Glossary di base per termini

…so we can have different cases

first case

first case …is it stable?

first case yes, it is stable!

second case …is it stable?

second case no, it is unstable!

Suggestion for your homework For each case, your answer could be: The ship shown in case … is … . In fact, when the ship heels, the centre of … shifts a lot/a little, and the hydrostatic force applied in … coupled with the weight forces applied in … creates a uprighting / capsizing / null moment. It is a safe/dangerous condition.

Homework for the next lesson For each of the following three cases, write on your copybook if they are stable, unstable or neutral, and and explain why. Then, other questions you should be able to answer orally (use this slides to help you to ansewer): - When is a body stable or not? - When, usually, is a system stable? - What happens to floating bodies as far as hydrostatic force and stability? - Why do large and narrow ships behave differently as far as stability?

Case A

Case B

…is it stable or not? …and why? Homework, 3rd exercise: Case C …is it stable or not? …and why?

Now a job for the next week lesson Now a job for the next week lesson. Work at home together with your deskmate and write together a short account. Answer to this question: “What in your opinion happened to this ship?” Some suggestions: - was this ship stable at the beginning? - maybe something unexpected caused a wide ship roll? - what type of ship is she? - probably ship's G has changed its position, and why? - Is she stable now?

Good luck!