There is a door, in a wall. This wall is located in my place of work. It helps define a room I usually need to pass through in order to get to my bicycle. This door and I do not get along. It tries to break my nose. Not actively. It’s more of a passive aggressive refusal to meet my perfectly reasonable expectations of doors, especially those attached to post and lintel constructs. This diagram should make my perfectly reasonable expectations perfectly clear:

Θ represents the angle of opening. P to indicates the power you are put into pushing the door open. Door indicates the door, and Wall indicates the wall.

For a boring, standard door that just swings on its hinges, we expect that P will remain constants and is independent of Θ, once the initial static friction of the hinge parts resting on each other is overcome. In this case, P is an input of force necessary to offset the loss of momentum due to kinetic friction between the moving hinge parts.

Many places of business, however, have doors that change how freely they swing depending on how open they are. Usually, the move much less freely when they are barely open. Reducing the speed of the door right before it shuts helps keep things quiet and helps keep our kids going to adulthood with ten fingers. In this case, P is inversely proportional to Θ.

We have a lot of these inversely proportional doors at work. The wicked portal in question appears to be one such door on the outside, thus my perfectly reasonable expectations. On the inside, however, the relationship between P and Θ are more complicated and non-linear.

A normal, inversely proportional door operates like the blue line. Part way through opening, but not far enough to let you pass through, the force required to open this particular door dramatically increases. Because my brain is expecting the door (Bad; red line) to behave like a normal door (IP; blue line), it likes to tell my feet to keep moving, even though the door has not yet gotten out of the way of my nose.

Fortunately, no one that I am aware of has yet been wounded by this vile door. I suspect that my co-workers are just smarter than me, or can learn. Me? Well, I’m just nimble, like a puma.

Author: Josh Witten

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