# Why does a sheet of paper stick to the end of a vacuum cleaner?

What makes a piece of paper or other material hard to pull away from the end of a vacuum cleaner once it's covering the opening? What force are you acting against when you try to pull it away? Also, why does the end of the vacuum cleaner stick to a wall, floor or other hard surface?

• Because it sucks!
– JMac
May 15, 2017 at 15:53

Suppose the piece of paper sticks to the end of your vacuum cleaner, and for simplicity let's assume no air passes through the sheet or on the sides of it.

The vacuum cleaner proceeds to suck air from the tube as long as it can with its limited capability. What it is effectively doing is reducing amount of air, and therefore the pressure, in the pipe.

This leads to a pressure imbalance: on one side of the sheet, there is air at the usual atmospheric pressure. On the other side, air at a slightly lower pressure. It's this difference in pressure that causes this force, which, in an ideal situation, is equal to the pressure difference times the surface of the part of the sheet attached to the top of the pipe, $F = S\Delta p$.

• so is it effectively the weight of all the air in the atmosphere pushing against the paper, with nothing pushing from the other side to cancel it out? May 15, 2017 at 15:56
• what about the case where it's against the wall or the floor - in which case it seems like the pressure shouldn't make a difference, because the surface is too solid to be moved by the air pressure? May 15, 2017 at 15:58
• Yes, I think you can say it's due to the weight of all the rest of the air. In the case of the wall, it's effectively the vacuum cleaner which is pushed against the wall by pressure, in a sense. The pressure of the region of air near the top of the tube, and near the wall, is lower then in the rest of the room. May 15, 2017 at 16:00

Like the fish that discovers water last, we don't normally notice the 15 pounds per square inch (psi) of atmospheric pressure that we live in. A vacuum cleaner can help us notice the air pressure without us having to jump out of our fish tank (Earths' atmosphere).

This pressure of 15 psi surrounds us and everything we touch. The vacuum cleaner reduces the pressure a little by constantly removing air from the hose, and this normally causes a focused wind that is useful for cleaning.

When a piece of paper blocks this wind, the pressure in the hose decreases further, down to some maximum pressure difference that the motor is capable of reaching. If it can drop the pressure to 14 psi in the hose, and the hose's nozzle has an opening of one square inch, then there will be one pound of force holding the paper on the nozzle. (I choose 14 psi to keep the math simple.)

This pound of force comes from more air molecules hitting the outside of the paper than the side that is looking into the hose.

As for the wall or the corner, it does not matter that the house has thick walls and that you can not tell where the full 15 psi is being applied. Nature finds it automatically.

Here is another way to look at it: Every part of the vacuum cleaner is exposed to 15 psi all around it except for the nozzle opening. The nozzle opening is only experiencing 14 psi. This is enough to cause the nozzle opening to press against whatever surface is blocking or slowing the airflow.

Another example: If you put a funnel on the opening you can increase the effective size of the nozzle opening. If the wide side of the funnel is round and six inches in diameter, then its area will be about 28 square inches. Unblocked, this will not do much. Now, use a bowling ball to cover this opening. A vacuum cleaner that can drop the pressure to 14 psi when no air is moving will now be able to generate 28 pounds of lifting force, letting you pick up the bowling ball via the suction alone. This fact was used by a vacuum cleaner company to show how strong their vacuum cleaners are, but I believe any other brand of vacuum cleaner could have done it too.

• thanks, i think that was what was counter-intuitive to me - just how strong normal atmospheric pressure is. May 17, 2017 at 9:03