Bernard Wilkinson, of Oamaru, asks :-

Why do mats move when placed on carpets ?

Daniel Schumayer, a physicist at the University of Otago, responded.

Everyday experience suggests that we can easily move, even slide, on smooth floors, e.g., wooden, varnished floor. It is then not too surprising that putting a mat over such floor the mat will start sliding as well. Simply there is not enough friction between the bottom of the mat and the smooth floor which could counteract the push when one steps onto or walks over the mat.

However, our common sense would dictate that putting two, non-slippery surfaces onto each other, e.g., a carpet and a mat, these surfaces should stick together fairly firmly and would hardly move. In the following I assume that someone in the family is not playing a trick on you and moving the mat while you are not watching.

If we put the mat on the carpet and record its position carefully, we may agree that we should not observe the mat moving. There is no reason that it should move. Therefore we can conclude that what might cause the creeping of the mat is that we step onto it and push its bottom, usually smoother, surface into the carpet and then release the mat when we step off the mat.

On the surface of carpets we find lots of long fibres. When the mat is pushed down, these threads tend to bend in the same direction determined by how the carpet was laid down. As the fibres bend, they slightly move the mat with them as well. When we step off the mat carpet fibers bend back to their original position, but there is no external pressure on the mat any more, the threads tend to simply brush the bottom of the mat, leaving it slightly off of its original point. This tiny effect occurs frequently enough and the minute slippage during walkovers add up and result in a noticable movement.

You can mimic the effect on a larger scale. Use an old toothbrush, which will act as the artificial carpet with long, brisky fibres. Put your finger on top of the bristles and press downwards. You will see that the bristles bend more or less in the same direction and your finger tends to move slightly in that direction. As you lift your finger slowly watch that the bristles slide back to their original position, while your finger now a bit off from its original position. What is even more interesting is that if you cut the head of the toothbrush off and put a small vibrating motor on it, you will see that this small robot moves! This is called a Bristlebot, see https://youtu.be/Q1zToREgV0c

However, if ever in doubt, just blame the dog or cat for moving the mat.

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