The great Danish physicist Niels Bohr once said: “If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet”. Clearly, Bohr was never a dedicated fan of the game of baseball, for if he had been, he would have been impelled to revise his statement.
While engaging in my nightly ritual of concertedly flipping between games in six different cities (thanks to the irreplaceable MLB Extra Innings cable package), I stumbled upon what appeared to be a serious seismic disturbance in New York City. Derek Jeter might be considered a baseball god according to the Yankee faithful, but quite clearly, only the fist of the true Almighty could have been responsible for such an occurance — Mr. Jeter’s successful sacrifice bunt was nothing but a bizarre coincidence. Seeking answers, I quickly retrieved D.E. James’ “The Encyclopedia of Solid Earth Geophysics”, but no sooner had I flipped to the index that an alternate camera angle revealed what had actually happened in Yankee Stadium on that Tuesday evening. The seismic activity was nothing more than an illusion caused by an impact to the netting behind home plate, which is directly coupled to the wire that supports a television camera.
The object that contacted the netting was, surprisingly, a living human being who many believe is lucky to still be alive at the time of this writing. Scott Harper, whose hometown of Armonk matches the state of his frazzled intellect in onomatopoeic fashion, had willingly plummeted some 40 feet from the upper deck to the netting below. Fortunately for him, the netting did not break and Harper was left shaken, but unharmed. Should we be surprised by this? Was Harper truly at risk for serious injury? Naturally, physics is able to provide us with valuable insight into these matters.
I estimate Harper’s mass to be 75 kg. When he made contact with the netting, he was travelling downward at a speed equal to the square root of the product of the force of gravity and the distance he fell. For a 15 meter fall, this corresponds to a speed of 12 meters/second on impact. Roughly speaking, this is slower than a head-on collision between two cars in a busy intersection, but faster than Jamie Moyer’s breaking pitches. At this speed, the impact force on the netting was only a few times Harper’s body weight, say, 3.0 – 4.0 mg. This is in the neighbourhood of 2500 Newtons.
From these simple calculations, the answer to our original question is now perfectly obvious, even to a freshman college physics student. For those readers who are not freshman college physics students, allow me to explain further. When landing near the center of the netting, Harper induced a tension in the thin ropes which comprise it. A dip of 45 degrees below the horizontal (surely an overestimate) would result in a tension of (2500 N)/sqrt(2) = 1767 N — for one rope only. This is the tension that would have been induced in a single rope had Harper been alert enough to grab onto it as he fell, like a bird coming to rest on a power line (albeit a much larger, suburban doofus species of bird on a wire). However, this type of netting was composed of many dozens of ropes, all of which shared this tension and supported the weight of impact. But the tensile breaking threshold of even one industrial strength netting rope is in the 2000 – 4000 N range, so therefore, several dozen of them could easily support the weight of not only one Scott Harper, but an entire “posse” of them.
I know what you are thinking, particularly those of you who are parents of undisciplined teenage boys. We have concluded that Harper was in no mortal danger, nor was he even close to it. Armed with this knowledge, you are fearful that many youngsters of like mind as Mr. Harper will attempt to duplicate his Yankee Stadium adventures. Even worse, they will be tempted to try it in groups of two or three or ten, young boys and young girls alike, or perhaps even mixtures of the two sexes all crammed on top of each other as if they were tumbling on a free-floating waterbed while engaging in playful groping before large TV audiences. Unfortunately for concerned parents, I will only lecture your children on matters of Newtonian dynamics, not matters of morals or the boundaries of appropriate behaviour. I may personally feel that Mr. Harper performed an act of dumbassery, but my primary responsibility is to communicate the principles of physics to the public. The numbers do not lie, and Newton’s laws do not judge. What the public — which includes overactive teenagers — chooses to do with this information is completely out of my control.