44 Types of Stability

Stable Equilibrium

If a structure is pushed out of we say it has been from equilibrium.  If the object tends to move back toward its position then it must be in a region of  and the force that pushed it back is a .

A marble sits at the bottom of a bowl. A marble moved up the left side of the bowl has an arrow pointing down and right, showing the direction of the net force on the ball
A marble in the bottom of a bowl is an example of stable equilibrium. Image credit: “Stable Equilibrium” by Urutseg, via Wikimedia Commons

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As your arm hangs from your shoulder, it is in . If your arm is lifted to the side and then let go it will fall back down to the hanging position. The hanging arm is a stable position because the of the arm is located below the , in this case the shoulder. When displaced (lifted a bit) the acting  on your arm will cause a that rotates your arm back down to the hanging position. In such cases, when an object is displaced from the equilibrium position and the resulting net forces (or torques they cause) move the object back toward the equilibrium position then these forces are called restoring forces. The sloth takes advantage of to save energy that humans spend on staying upright. If the sloth is displaced in any direction, the force of gravity automatically acts as a restoring force and returns the slot to its position.

A two-toed sloth hangs from its feet in a stable equilibrium position. Image Credit: Two Toed Sloth by Cliff via Wikimedia Commons

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Unstable Equilibrium

When a system in is and the resulting pushes the object even further away from the equilibrium position then it must have been in an . Technically, real systems cannot spend time at unstable equilibrium point because the tiniest vibration will cause them to move out of equilibrium not to mention that you could never place them perfectly into position in the first place. Trying to balance a marble on a hill is a good example:

A marble sits at the top of a spherical hill. A marble moved down the left side of the hill has an arrow pointing down and left, showing the direction of the net force on the ball.
An example of unstable equilibrium is a marble placed on a hill. Image Credit: “Unstable Equilibrium” by Urutseg, via Wikimedia Commons.

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Metastable Equilibrium

Some structures that are in and can be relatively far before they are no longer in . Other structures structures that only require a small displacement to move out of equilibrium (like toddlers). We often call these systems stable and unstable, but this can be misleading because any standing structure is somewhat stable and a truly unstable structure would not stand still for any time. These structures that are in a stable region, but could be pushed passed a tipping point are known to be in a .

A marble sits at the bottom of depression at the top of a spherical hill. A marble moved down the left side of the hill beyond the depression has an arrow pointing down and left, showing the direction of the net force on the ball.
The marble is in meta-stable equilibrium as long as it doesn’t move outside the dip in the center. The peak at edge of the dip is analogous to the tipping point for a structure; beyond this point the marble will not move back toward the equilibrium position. Image credit: “Meta-stable Equilibrium” by Urutseg via Wikimedia Commons

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Keeping your balance requires that you stay with the the stable region of a .  For example, we expect that most people would say the person balancing on their head in the following image is unstable, but that wouldn’t be quite accurate. Actually, the person is actively adjusting the shape of their body to shift their to remain within the stable region of a , though it is a narrow one.

 

A person balances up-side down on their head on the top of a glass wine bottle.
A person in a barely-stable equilibrium. Image Credit: Usien via Wikimedia Commons.

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Exercises

 


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