# Sliding ruler on table top

I've got a standard foot-long flat plastic ruler (about an inch wide) and a desk with a smooth formica-like surface. When idly passing time reading on the computer, I will pick up one side of the ruler (keeping one of the four edges still leaning on the table) and drop it to see how far it will slide. It can travel about a foot before stopping. Why is it sliding? It doesn't slide nearly as far if I give it a little push. Has it trapped some air temporarily between the ruler and the table? And does it stop because it is hitting some irregularities on the table? Or because it has rolled off all of the trapped air molecules? Thanks.

## 3 Answers

This sounds like it's an example of ground-effect. When landing a standard fixed wing aircraft (from experience, a 2 seater Cessna) the aircraft descends at a constant rate towards the runway, assuming that the controls and engine power remain fixed. However, a few metres above the runway this descent slows dramatically - the point where you thought you'd touch down sails past and you continue to "float". You can continue for a considerable distance before finally sinking to the ground.

What's happening is the ground is providing a barrier to the higher pressure area under the wing (ruler), so it doesn't dissipate as it would in normal flight. Essentially, your ruler may be acting as really low-tech hovercraft for a few moments.

See the "Ekranoplan" for an extreme application of the principle.

• Nice answer. I've never heard of this. Not sure if this is the right answer but it sure sounds like it could be. Thanks. – John K. May 26 '16 at 14:14

In a vacuum the bottom end (part touching the table) will move away in order that the center-of-mass in the horizontal direction remain the same. Starting from a near-vertical position, this would account for about 6 inches of movement. I think you are right about the air, though.

• Doesn't the horizontal component of the reaction force between the end of the ruler and the table accelerate the C of M ? – DJohnM Nov 12 '13 at 0:38
• Momentum would not be conserved in that case. – lionelbrits Nov 12 '13 at 1:43
• I think he is holding one end, giving the cm the forward momentum it needs to slide across the table. – ja72 Feb 10 '14 at 17:27
• @User58220 In the absence of friction, there is no horizontal component of the reaction force. (So far, we haven't addressed the role of friction in this thread.) – garyp Mar 12 '14 at 13:13

If you did not implant a horizontal impulse on the ruler and there was no friction then the centre of mass of the ruler would fall vertically and so one end of the ruler would move forwards and the other end backwards but the centre of mass of the ruler would stay in the same position.
If there was friction between the ruler and the surface then the centre of mass would be horizontally displaced in the same direction as the frictional force. The ruler would move further in one direction than the other.
In the extreme case one end of the ruler would not move at all whereas the other end would move six inches horizontally.

The fact that the ruler moved a significant distance implies that you gave the ruler a horizontal impulse and that the frictional force was small. Thus the centre of mass did move in a horizontal direction due to the horizontal impulse that you gave it whilst the ruler was falling.

Even on a smooth glass surface I could not get my ruler to move any more than about four inches however what I did notice was that towards the very end of its fall the end in contact with the surface changed direction. This appears to be consistent with the idea of a frictional force acting in the opposite direction to the horizontal motion of the end touching the surface and hence moving the centre of mass horizontally in the direction of the frictional force?

## protected by Qmechanic♦May 26 '16 at 5:39

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