Thingiverse
Sliding Ladder, Ellipse by lgbu
by Thingiverse
Last crawled date: 4 years, 1 month ago
Sliding/Falling Ladder
The sliding ladder is a classic problem in school mathematics. Depending on the location of the person, the falling trajectory is either an ellipse or a circle (a circle is a special case of an ellipse, of course). Three pencil holes are made on the ladder (1/4, 1/2, 3/4) for tracing part of the curves.
Two designs are provided. The circular sliders can be printed together with the rails. After some physical modeling, one should attempt a proof. Here are some basics: (1) the ladder has a fixed length; (2) right triangles are interesting (the Pythagorean Theorem); and (3) there are a bunch of similar triangles in the background. Have fun!
References
https://demonstrations.wolfram.com/PhysicsOfASlidingLadder/
http://physics.princeton.edu/~mcdonald/examples/ladder.pdf
The sliding ladder is a classic problem in school mathematics. Depending on the location of the person, the falling trajectory is either an ellipse or a circle (a circle is a special case of an ellipse, of course). Three pencil holes are made on the ladder (1/4, 1/2, 3/4) for tracing part of the curves.
Two designs are provided. The circular sliders can be printed together with the rails. After some physical modeling, one should attempt a proof. Here are some basics: (1) the ladder has a fixed length; (2) right triangles are interesting (the Pythagorean Theorem); and (3) there are a bunch of similar triangles in the background. Have fun!
References
https://demonstrations.wolfram.com/PhysicsOfASlidingLadder/
http://physics.princeton.edu/~mcdonald/examples/ladder.pdf