Silhouette of Passage

 When a cartoon character smashes through a solid wall or other object, we see the perforation as the crisp outline of the character. What would a condensed matter physicist say about this cookie cutter type of material response?

Answer

The condensed matter physicist knows a lot about the physical properties of liquids and solids, so he or she probably would say, “Wow! How was that done?” The only realistic possibility is that the wall cut should be quite messy and the cartoonist cleaned the edges for heightened dramatic effect!

We can estimate how difficult the cookie cutter hole would be to achieve by considering a ball thrown at the wall. The impact surface area increases rapidly in time as the ball and wall both bend a little during the collision. The initial kinetic energy of the ball just before the collision becomes distributed in the distortions of the ball and the wall. The interactions between the molecules of the wall material change as some of the available energy from the collision spreads from the immediate impact area. If the total collision time is extremely short, the energy distribution will be quite limited in distance, and much of the energy is available for ripping. Otherwise, if the collision time is much longer, a big portion of the wall will respond by deforming just a little, and ripping may not occur.

A bullet going through the paper at a practice target makes a fairly clean hole for two reasons: (1) the contact time is extremely short; (2) the bullet offers a nearly round profile, so there is symmetry about an axis perpendicular to the hole. Even then, close examination of the bullet hole reveals an irregular surface and additional tearing beyond the actual round hole. You can check out the advantage of a symmetrical object. Now, with appropriate safety precautions, try to rapidly push any shaped profile other than round through a sheet of target paper. The lack of cylindrical symmetry perpendicular to the surface usually creates enormous problems for the material because slightly more energy goes into some directions. Moreover, tearing is required to occur at different distances along a noncircular profile, so there may be points where the transferred energy density is significantly higher or lower than the surrounding paper regions. All these factors and several more act against a very clean cut through the material. The cut through a thicker piece of paper or a wall that has significant depth would be even messier. Of course, the cartoon character has several other options for getting through the wall when time permits: (1) simply paint an exit onto the wall through which only he can pass, or (2) the character can carry around a hole to be affixed where needed!

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