Stability and its Application

Stability
Objects have a certain amount of stability, where they can withstand a certain amount of tilting before they topple over. The diagram below shows three stages of a brick’s tilt:

• If you tilt the brick slightly (diagram a) and then release it, the turning effect from the brick’s weight returns it to its upright position
• If you tilt the brick a bit further (diagram b), you will find that there is one position that it can remain balanced on one edge. This happens when the centre of mass is directly above the edge on which it is balancing – there is no turning effect exerted in this position
• If you tilt the brick even more (diagram c), it will topple over upon release. This happens because the line of action of the weight is “outside the base” of the object (in the diagram you can see this because the arrow showing weight rests outside the two lines at the base of the rectangle)

A lot of objects can topple over very easily, which is why some are manufactured especially to prevent toppling over. Examples include tractors – think about how wide apart their wheels are and how low the engines are kept. Because the centre of mass is in the engine, it is kept low so that the tractor has to tilt an awful lot for the line of action of the weight to fall outside the base – and even if it did, it is pushed back further by the fact the wheels are incredibly distant to each other. Safety is another huge factor in toppling – take buses and coaches for example. They have to go through tilt-tests before they are allowed on the road to see how much they can tilt before toplling over. These test are important because it has to be able to drive along hilly roads and turn through sharp corners

STABILITY

Let us investigate the stability of an object placed in three different positions as shown.

Three positions of stability
In the first position, if the object it tilted a little, it will fall back to its original position. This form of equilibrium is called stable equilibrium. The weight which acts through the centre of mass, creates a clockwise moment about the point of contact of the object with the ground. This clockwise moment cause the object to return to its original position.

Stable equilibrium
In the second position, if the object is tilted a little, the object will topple. This form of equilibrium is called unstable equilibrium. As it can be seen, the weight creates an anti-clockwise moment about the point of contact. This anti-clockwise moment cause the object to tilt further from its original position until it finally topples.   The last position is called neutral equilibrium. The object stays in its new position if it is displaced slightly. The weight acts directly at the point of contact and no net moment is created to displace the object further.

Neutral equilibrium

APPLICATIONS OF STABILITY

As can be seen from above, an object is stable if its centre of mass is low and it is unstable if its centre of gravity is high. Due to this reason, machines which require stability are purposely designed with a low centre of gravity, for example a sports car. In a long distance coach, the luggage of its passengers are placed at the bottom of the coach rather than top as in an aircraft. This is to ensure that the centre of mass of the coach remains low with the luggage so that the coach do not turn over when it is moving.

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