Modeling a Bead on a Function

The block-on-a-linear-ramp problem is a standard introduction to vectors, gravity, friction, normal force, and Newton's laws in first-semester physics; computational modeling of this problem is also an excellent way to teach programming to beginners. Here, we look at moving this sort of problem to more advanced coursework by modeling the behavior of a bead on a wire which is described by any function. This allows for the incorporation of calculus into programming and the visualization of variable motion and forces.