Curved flexible sheet creating a flip flop, valve, or flap

I saw a classmate recognize this in class once and he was showing it to our Physics teacher. Hold a piece of paper in your hand on the side like you're grabbing a plate or the side of a tray and curve it using your fingers and thumb on either side of the paper. Then drop something on the other end of the paper. If you orient the paper concave up, the object will be caught inside the scoop shape. If you orient the paper concave down, the object will collapse the arch shape and drop past the paper onto the table.

Concave up....

...catches the object.

 Concave down...

 ...lets the object fall past as the paper bends. Usually the object slides down one of the sides of the arch too, so you'd have to account for that in a practical application.

This reminds me of a flip-flop, valve, or flap, such as the ones seen in sorting machines or marble machines.
You could make this with a material that is a little more stiff and predictable, like rubber or a flexible plastic. The flap could be rotated with a motor or a rotating pneumatic actuator. It could be angled so that when an object gets caught on the concave up side it slides down and away like in a channel.
However, the same actuator that rotates the flap can be used to direct objects much more simply. The two-way action could be done with a stiff, spring loaded flap that is kept from moving one way with a stopper or ledge, like a door jam, and able to freely open in the other direction.  So this flap design must be uniquely beneficial for the resources of an actuator to be used up in this way.

One beneficial example I've thought of (which doesn't even require an actuator) is a door into a container that keeps objects from getting out (concave up side faces inside container), but lets objects in (concave down side faces out). This container could be vibrating or tumbling the objects inside, so a one-way opening is needed. The container might be naturally round, like a tire, so this concave flap could be built into its geometry, instead of being an abnormality like a square or circular door.

Search sorting machine on Youtube, or Lego sorting machine.

Related marble machine flip flop:
http://www.sentex.net/~mwandel/marbles/flipflop.html