Suction Cups

Sorry, no clever title this time; I've been feeling pretty crummy the last few days, so I haven't been as active here as I'd like.  Last time I promised a little talk about suction cups, so here we go...

Suction cups work by creating a low-pressure (or ideally vacuum) chamber, which is then maintained by the outside air pressure.  We'll make a few simplifying assumptions about the suction cup: it stays perfectly conical, and its surface area remains the same.

The surface area of the cone is given by

or, solving for r^2,

Meanwhile, the volume is

Combining these and simplifying gives

Plotting this gives

 

The maximum on the plot will be the height with the smallest internal pressure (volume and pressure are inversely related).  That means that after pressing a suction cup down to evacuate as much air as possible, pulling it up slightly will create a stronger grip.

I'm actually feeling a bit better having written this up, so maybe I just needed more brain-exercise...