The phenomenon of the ruler trick

[Anonim2831]

Homework Statement

hey, I'm wondering about the phenomenon of the experiment with a ruler and a piece of paper. Description of the experiment: we place a ruler on the edge of the table (one end of the ruler protrudes beyond the table) and then we place a piece of paper on it. When we throw the ball at the protruding end of the ruler, the ruler will not fall (it will be held by the paper). If we know the length of the ruler (protruding and not protruding), the mass of the ball and the surface of the paper, how can we calculate from what height the ball should be thrown in order for the ruler to fall or break?

Relevant Equations

The equations that will be needed here are certainly pressure, forces, and possibly energy, but I don't know where to start

WI know that the phenomenon occurs due to the decrease in pressure under the sheet of paper.There is therefore greater pressure above the sheet of paper, pressing down on the sheet of paper, which prevents the ruler from tearing off. However, I lack patterns and specifics

 

[Hill]

I'd assume that the force holding paper from moving up is momentarily about 1 atm times the area of the sheet of paper.

 

[Anonim2831]

M I think it may be so, but I don't know how it will help me calculate the height from which I need to throw the ball

 

[Hill]

... possibly energy...

Possibly momentum?

 

[bob012345]

Homework Statement: hey, I'm wondering about the phenomenon of the experiment with a ruler and a piece of paper. Description of the experiment: we place a ruler on the edge of the table (one end of the ruler protrudes beyond the table) and then we place a piece of paper on it. When we throw the ball at the protruding end of the ruler, the ruler will not fall (it will be held by the paper). If we know the length of the ruler (protruding and not protruding), the mass of the ball and the surface of the paper, how can we calculate from what height the ball should be thrown in order for the ruler to fall or break?
Relevant Equations: The equations that will be needed here are certainly pressure, forces, and possibly energy, but I don't know where to start

WI know that the phenomenon occurs due to the decrease in pressure under the sheet of paper.There is therefore greater pressure above the sheet of paper, pressing down on the sheet of paper, which prevents the ruler from tearing off. However, I lack patterns and specifics

It seems to me the problem is very ill defined. How about a drawing or details about the system or better yet, the actual problem as described in your book.

 

[Lnewqban]

https://www.eecis.udel.edu/~vijay/BLAST/air_pressure/newspaper_ruler.html

 

[diogenesNY]

I think it is worth observing that there appear to be a _very large_ number of variables at work in this demonstration. Consequently you would have to travel down many rabbit holes to begin, even assuming a somewhat loosey-goosey level of precision. One or even several equations will unlikely be sufficient.

 

[haruspex]

First consider what the paper is doing. Without the paper, air can easily flow under the ruler, maintaining atmospheric pressure on both sides. The paper inhibits this, but does not stop it completely. This makes an accurate analysis very difficult, so suppose the air is entirely prevented from coming under some area and see how big an area is needed.

The ruler will lift off the table through some small angle $\theta$. Given air pressure acting uniformly over a rectangular area covering the ruler of given length and width, how much energy is needed?