Springs Part 2: Projectile Springs

One of the first topics that’s covered in most introductory physics course is projectile motion, which describes the trajectory of an object subject only to gravity. Such an object always follows a parabolic arc, meaning that its trajectory in the air is perfectly described by a second-degree polynomial. The parabolic shape of the trajectory arises from having a net force (and therefore acceleration) that points purely in the downward direction while the object has some horizontal component to its velocity.

Interestingly, when beads connected by springs reach equilibrium, they also settle on the shape of a perfect parabola. This effect is more noticeable when you have many beads as shown below.

Can you rationalize why beads on a spring settle on the same shape as the trajectory of a projectile? Think about the net force on each bead when the system has reached equilibrium.