Stable unstable and neutral equilibrium

Stable unstable and neutral equilibrium

A child playing with a pencil soon learns that it is scarcely possible to make it balance on its point. On the other hand, it is comparatively easy to make the pencil stand upright on a flat end.In order to understand the difference between these two cases let us consider a wooden cone placed on a horizontal table. A cone cannot be made to stand on its tip.

]Theoretically, this feat might be possible if the cone could be placed with its centre of gravity exactly in a vertical line through the tip. The cone would then be in equilibrium under the action of the force of gravity, mg, on it acting downwards and an equal and opposite reaction to its weight exerted on it by the table. But even if this condition could be achieved momentarily, the slightest vibration or fraught would inevitably cause the cone to tilt. (The force of gravity. mg ; would then exert a turning force about the tip, and this would cause the cone to topple over (Fig. 6.14 (a)). A cone placed on its tip is said to be in unstable equilibrium.

Stable, unstable and neutral equilibrium
Stable, unstable and neutral equilibrium
Stable unstable and neutral equilibrium
Stable unstable and neutral equilibrium

Fig. 6.14 (b) shows the cone standing on its base. It tilted from this position, even
through a fairly large angle, the vertical line through the centre of gravity, G, will still fall inside the base AB. Consequently, the force of gravity on the cone will have a moment mg x x about an edge of the base which will pull the cone back into its original position. Under these conditions, it is not easy to knock the cone over, and it is said to be in stabLe equilibrium. In Fig. 6.14 (c) the cone is lying on its side. The base is now simply a straight line, and if the cone is rolled into a new position the vertical line through the centre of gravity still continues to pass through exactly the same point in the base. Whatever the position of the cone, the reaction from the table will act in the same traight line as the force of gravity through G, and so the cone will be in equilibrium. The force of gravity exerts no moment about the base as axis and, if displaced, the cone will therefore remain at rest in its new position. This condition is described as neutral equilibrium.

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