## Balancig the Pipe

The exhibit here has three pipes of different lengths. Place your palm against the bottom of each pipe and try to gently lift and balance them – one at a time. Which of the three pipes is the easiest one to balance? The longest one!

In order to balance the pipes one has to suitably shake the palm- faster for shorter length. Therefore, balancing the longest pipe is easier than balancing the shortest one.

In this exhibit, there are three tubes, each having a ring like structure attached at the top. The tubes are identical in all other aspects except for their lengths. The task here is to lift the tubes and balance them on the palm. Most of the people would prefer to lift and balance the shortest tube. When the tubes differ only in the length and are identical in all other aspects, the shortest tube would weigh the least. This fact would trigger to prefer the shortest tube. But when actually tried, one can notice that it is too difficult to balance the shortest tube and in fact it is the longest tube which is the easiest to balance in spite of it being the heaviest of the three.

These tubes that are pivoted at their base and standing upright are like inverted pendulums. They have their own natural frequencies depending on their lengths. The longer the tube, the lower will be the natural frequency and vice versa.

That means when held on the hand, the shorter tube makes more back and forth motion than the longer tube (whose natural frequency is less comparatively). Therefore, in order to balance the tube one has to shake the hand very fast. This requisition of vigorous shaking makes the balancing act extremely difficult.

On the other hand, the longer tube with a lower natural frequency also does move back and forth but much slower than the short tube. Thus, the shaking of hand need not be so vigorous. Therefore, it is easier to balance a long tube.

One other interesting aspect here is the role of the ring like structure at the top of the tube.

A tube of uniform mass distribution will have its centre of mass along the axis at a distance equal to half the length from the base (actually from both the ends). By introducing the ring structure at the top, the centre of mass shifts up. Because of this, the equivalent length of the pendulum, which is the distance between the point of pivot and the centre of mass, is now much longer.

That means, the natural frequency of the tube loaded at the top is lower than that of an unloaded tube.

That implies that loading the tube at the top would make it much easier to balance.

### Website Visitor counter

'Mondays and Second Tuesday are holidays'