Dot Physics

Check out this thing.

That is where the guy (Jem Stansfield of BBC's Bang Goes the Theory) shows how he built this thing. Here is part 2 where he uses it to climb a building.

Here are some questions:

• Why does it not matter how powerful the vacuum is?
• How does a vacuum cleaner work anyway?

How does the vacuum cleaner work?

I know this is not HowStuffWorks.com, but I guess I should show some stuff. The cool thing about a vacuum cleaner (think shop vac so that I don't have to deal with the brushes) is that it is just one thing - a fan. The fan essentially moves air out of the vacuum part of the cleaner so that it "sucks". Here is a diagram for a vacuum cleaner with no hose (no air input).

So, the fan pushes air out of the chamber. It does this by hitting the air with the fan blades. The result is less air inside the chamber than outside. The wooden board on the cover of the hose is pushed there not by the air inside the vacuum, but rather by all the air outside (due to the atmosphere).

In a normal use, air comes in that part of the vacuum - hopefully bringing dirt and stuff with it. Note that I left out important parts of the vacuum cleaner if you want to use it to clean - namely a filter. But..how does the guy use the vacuum cleaner to lift himself? Here is a diagram of a board similar to what the guy created and stuck to a ceiling.

Let me assume that the mass of the board is small enough to be ignored. If this is the case, I can look at three forces acting on the board.

• The tension in the string from the big weight hanging on the board (the load)
• A force pushing up due to the atmosphere (which is outside the space between the board and the ceiling)
• A force pushing down on the board due to pressure of the air inside the space between the board and the ceiling

All of these forces are in the vertical direction - so it is a one-dimensional situation. If I know the pressure of some gas, then the force it exerts on a surface would be:

Here if the pressure is in Pascals and the area is in meters², then the force will be in Newtons. If the board is in equilibrium, then:

The P_vacuum is the pressure inside the vacuum chamber (just to be clear). From the video, the goal was to calculate the area of the board such that it could support his weight. In the video, Jem claims that even cheap vacuums "pull with a fifth of a vacuum". He also says that is "a suction force of a kilo for every 5 square centimeters". Yes, he made some mistakes there - but the real question: is he talking about the net force? Ok, let me start with 1/5th of a vacuum. Maybe he means that the net pressure on the board is 1/5th of what it would be if the inside of the chamber had no pressure. In this case the pressure inside would be:

If I look at this the other way, (5 kilos per 5 cm²) what would the vacuum pressure be? First, it should be noted that 5 kg, is the mass. The weight (and force) would be 49 Newtons. The area in m² would be 5 x 10^-4 m².

Problem. 20,000 Pa is not 2,000 Pa. Ok, one more try. I found this in the video:

I have another shot that looks a little better. This is his gauge that he sticks in vacuum cleaners to test them. I am pretty sure it reads about -5.2 in Hg - this is a pressure measurement (inches of mercury). According to my unit conversions, this would be around 18,000 Pa. Ok - so I think the problem is a confusion between pressure and gauge pressure.

Gauge pressure is the difference in pressure between the inside of the thing and the atmosphere. So, a gauge pressure of zero would mean that the pressure inside the thing and outside the thing (whatever that thing may be) is the same.

The gauge reads 18,000 Pa - obviously, the gauge pressure. This agrees with the 1/5th of a vacuum thing. I think the 5 kilo thing he was saying was how regarding atmospheric pressure.

How big of an area would be needed to support a 70 kg person?

This would be a square about 20 cm x 20 cm. Seems about right.

Why can you use a cheapo vacuum cleaner?

In terms of "suction", what is the difference between a cheap and an expensive vacuum cleaner? They might have about the same pressure in the chamber (when the hose is blocked), but the expensive one will have a much higher flow rate. It will probably have a bigger, or faster fan. This is important if you are using the vacuum to actually clean stuff because it is this flow of air that takes dirt with it. If you are using the vacuum to fulfill your childhood Spider-Man dreams, a cheap one will do fine.

How is it possible that cheap old vacuum can lift that guy? Answer: it doesn't. First, the board does not really move - so no work is done on the person (Work = F dot Delta r). All the vacuum has to do is move some of the air out of the space between the board and the wall.

I am seriously considering building something like this - just to hang on the ceiling.