Day 43: Elliptical Conundrum
For their capstone, a pair of students wanted to do a video analysis of a marble going around the inside of a circular hoop and an elliptical hoop. They wanted to see how the speed changed as the marble traveled. They thought the marble would travel at fairly constant speed in the circular hoop, but would gain speed as it whipped around the tightening curve of the ellipse.
Although I knew that wouldn’t be the case, what they found surprised us all: the marble in the elliptical hoop decelerated much more rapidly than in the circular hoop.
(The photo shows us trying to reason it out with geometry. Does the elliptical wall’s normal force not act at a right angle to the marble’s instantaneous velocity?)