Bouncy Candy

Why does a tic-tac sometimes bounce higher than its previous bounce?

Take a look at Figure 1. This is the well known shape of a tic-tac. Sometimes, when a tic-tac is dropped, it's third bounce reaches a greater maximum height than that of the second bounce. Today's article will explain why this is possible.

Figure 1

Figure 2

The tic-tac scenario goes against our intuition. For example, when someone drops a ball, each bounce is shorter than the previous one (Figure 2). This seems obvious to us, but we should think more about how this works before moving on.

There are two main types of energy involved in the bouncing of the ball. There is gravitational potential energy (GPE) and kinetic energy. GPE is associated with the height from the surface. On the other hand, kinetic energy is associated with movement. The faster an object moves, the more kinetic energy it has. When the ball is at the top of each bounce, the kinetic energy is small and the GPE is large. When the ball approaches the surface, the GPE comes close to zero and the kinetic energy increases.

So why is the height of each consecutive bounce of the ball shorter? We've established that when the ball bounces, kinetic energy and gravitational energy switch back and forth between each other. As the ball goes higher, the kinetic energy becomes GPE. The ball reaches the peak of the bounce when all of the vertical kinetic energy has been exhausted into GPE. It follows that less vertical kinetic energy means a shorter bouncing height. Therefore, each bounce of the ball loses vertical kinetic energy. This happens because when the ball collides with the ground, the energy is lost to things like heat and sound. The same exact process happens with the tic-tac. So how is it possible that one bounce can go higher than the previous one?

Figure 3

At this point, let's watch a video of our scenario (Figure 3). You may have noticed a difference in the two bounces. In the short (first) bounce, the tic-tac is spinning fast. For the higher (second) bounce, the tic-tac is spinning slowly. Now is a good time to bring up a third piece of the puzzle. Rotational kinetic energy. This energy is associated with the spinning of an object. In the first bounce (fast-spinning), there is much more rotational kinetic energy than the second bounce. In the first bounce, the rotational kinetic energy is kept relatively constant throughout the motion, while the vertical kinetic energy turns into GPE at the peak. During the ball-surface collision between the first and second bounce, the rotational kinetic energy is translated to vertical kinetic energy. This extra energy is translated to GPE which will sum up for more GPE than the first bounce. This is the reason why the second bounce is able to go higher than the first in spite of losing energy to the collision with the surface.