Cartoon Stretching

Objects in cartoons are stretched and squeezed into amazing distortions and then released. Some of the characters suffer the same fate. When the body material of a cartoon character is being pulled, we often see the part closer to the applied force stretch first and then the rest follow with a small time delay. For example, a cartoon dog may pull on a character’s leg, which we see being stretched while the torso remains normal, until finally the torso stretches, the arms stretch, and the character releases his or her handgrip from the doorway. Using some physics concepts, what can you say about the speed of sound in a cartoon character’s body?

Answer

There are many ways to approach the problem of determining the speed of sound in the cartoon character’s body. We consider one approach only. Start with the application of an external force to the surface of the body at some location the character’s foot, say. We see the stretch region progress up the leg over a period of one to two seconds.

“Wait just one minute!” you exclaim. How is the speed of sound in the material related to its speed of stretching in response to an applied force? The answer is that both processes require communication from one molecule to the next molecule outward, from the applied force region to the far reaches. Usually the much smaller energy in the sound application produces a very tiny stretch followed by a relaxation and overshoot, then another stretch, etc., repeatedly at some frequency above 14 Hz or so. The stretch produced by the tug of a much larger applied force shows a much larger displacement of the molecules that may or may not relax when the applied force is lessened. The larger displacement between molecules for the stretch process may require slightly more time if the process cannot be modeled by a collection of linear harmonic oscillators, but the speed of stretch will be very close to the value of the speed of sound for most materials.

The stretched cartoon character’s body exhibits a communication speed of about a meter per second, a very slow speed of sound indeed when compared to most materials, which have a speed of sound of about 300 meters per second. So we conclude that cartoon characters are made of very unusual materials. Perhaps designer materials in the future will be able to mimic a cartoon material. According to the world’s greatest detective, the game is afoot!