EXAMPLE 8 Falls

Area-volume tension affects how animals respond to falling, another of gravity’s effects. How come a mouse may be unharmed by a 10-story fall, and a cat by a 2-story fall, but many humans are injured by falling while running, walking, or even just standing?

The explanation is that the energy acquired in falling is proportional to the weight of the falling object, and hence to its volume. This energy must be absorbed either by the object or by what it hits, or must be otherwise dissipated at impact—for example, as sound. The fall is absorbed over part of the surface area of the object, just as the weight of the cube was distributed over its base. With scaling up, volume—hence weight, hence falling energy—goes up much faster than area. As size increases, the hazards of falling from the same height increase.