The roller coaster

During the curve lecture, we demonstrated a roller coaster. One can learn a lot from it. The roller coaster is made of a curve. The ball is lifted up along a spiral curve, the ball motion id described by a parametric equation which leads to velocity, acceleration, TNB frame etc. When building the coaster one has to take care of f(r(t)), the height function which relates to the potential energy of the ball. By looking at energy considerations alone, we can decide from any curve, whether it is a valid coaster configuration that is a curve for which the ball moves along a closed loop as in the picture.

M4V, Ogg Webm.