Physics · Ch 4 — Laws of Motion
Stable, Unstable and Neutral Equilibrium
Stable, Unstable and Neutral Equilibrium
A body resting under the action of balanced forces is in mechanical equilibrium, but there are three qualitatively different TYPES of such equilibrium, distinguished by what happens when the body is slightly disturbed (Fig 4.10).
STABLE equilibrium: if slightly displaced and released, the body tends to return to its original equilibrium position (e.g. a ball at the bottom of a bowl-shaped dip). Here the potential energy of the system is at a local MINIMUM.
UNSTABLE equilibrium: if slightly displaced, the body moves progressively FARTHER away from its original position, never returning on its own (e.g. a ball balanced at the very top of a dome/hill). Here the potential energy is at a local MAXIMUM; once disturbed, the system 'falls' towards a configuration of lower potential energy.
NEUTRAL equilibrium: the potential energy of the system is CONSTANT over some region/plane, so even after being disturbed, the body remains in equilibrium at essentially any new position within that region (e.g. a ball resting on a perfectly flat, horizontal surface). …
What this figure shows. Three simple side-view sketches of a ball resting under gravity in different surface shapes, each representing balanced forces (equilibrium). Part (a), STABLE equilibrium, shows the ball sitting at the bottom of a concave (bowl/valley-shaped) curved surface or dip -- if nudged sideways it would naturally roll back down to the same lowest point. Part (b), UNSTABLE equilibrium, shows the ball balanced precariously at the very top of a convex (dome/hill-shaped) curved surface or hump -- if nudged even slightly it would roll away and down, never returning. Part (c), NEUTRAL equilibrium, shows the ball resting on a perfectly flat, horizontal surface -- if nudged sideways it simply rolls to a new position and stays there, equally at …