The Projectile Inside the Loop

The loop-the-loop demonstration is one of the favorite toys used in introductory physics courses. In this simple device a small sphere typically rolls down an incline and then continues around a circular track, which constitutes the “loop.” By using the principle of conservation of mechanical energy, students are usually asked to find the initial conditions that enable the moving body to “safely” make it around the loop. At times, I tried to ask my students an unusual question: “What happens to the body if it doesn’t go around the loop and falls inside it?” In this paper I will detail the answer to this question and describe a simple experimental activity related to this interesting problem.

The student answers are usually contradictory. Some suggest that the object would simply fall straight down, after loosing contact with the rail of the loop. Others suppose that the body would continue to follow a somewhat circular trajectory in the air, with a different radius of curvature, compared to the loop radius. In general, many students fail to recognize that the object, once the contact with the rail is lost, simply follows the kinematical rules of a projectile motion.