Imagethief was an indifferent student in high school. My success in any given class was dictated by my level of personal interest in the topic. So I did OK at biology, which I liked, great in English and composition once I found a class that wasn’t numbingly dull, and appallingly in math, which held no appeal for me at all. God bless the University of California for weighing SAT scores so heavily in 1984, because if they only looked at my grades they probably would have assumed I applied by mistake and not even bothered to send me a rejection note. But, befitting someone who lives in China, I was a brilliant test taker and thus built the foundation for the success I enjoy to this day, such as it is.
Among the courses I blew at was physics, in which I eked a passing grade out by minuscule fractions of point. My problem with physics was that it was largely math, in which I already had little interest, and I really couldn’t see how any of it was going to be relevant to the rest of my life. I mean, figuring out planetary orbits? Isn’t that what NASA is for?
Life is, of course, all physics, as we discover when we get older and start banging into things. Not that it would help me to be able to work out how many newtons of force are generated when I bang my shin into the coffee table, but at least I’d have a layer of academic appreciation to filter the curse words through. This would be important as I have a young son who has (biology again) the three-year-old’s stupendous capacity to remember all words he hears and repeat them at inopportune times, like in front of his grandmother.
Children are also a regular reminder of influence of physics in daily life. Ballistics, gravity, impact, thermodynamics, and, during the diaper years, even radioactivity. My son is the remedial version of the high school physics class I doodled my way through all those years ago. This became apparent a week or two ago when we went down to Houhai to fool around on the ice. I generally enjoy a day on the frozen lakes once or twice a year, although it can get a bit nasty close to the thaw when a season’s worth of dead fish and turtles emerge from entombment. This year, we figured Zach was old enough to appreciate it as well. We didn’t do anything as silly as putting him on ice skates, or letting him walk around on the ice. Instead, I rented one of those sled-chairs that you nudge along with a couple of slender, metal poles. The chairs seat two people, so I put Zach in front and went stroking off across the ice.
People who haven’t tried them don’t appreciate how rigorous using the sled chairs is. The little poles are designed to make your hands cramp, and the chairs offer a spectacular combination of fairly high speed and a complete lack of steerability. The lakes get pretty crowded on midwinter weekends, and frankly it amazes me that more people don’t wind up in the hospital with chair runners through their calf muscles.
But you don’t have to have a collision to get in trouble with the chairs. You can get in trouble all by yourself. I discovered this when I had a brainstorm to make the chair spin in place. Now, this is where the physics really become interesting. I’d like to introduce you to two equations that I know were covered in my high school physics class, but which I dismissed at the time as being completely irrelevant to any experience I’d ever have.
First is the equation for centripetal force. This is the force that makes a body follow a curved path, and is often mistakenly referred to as “centrifugal force.” In the absence of a centripetal force, an object previously following a curved path will suddenly fly off on a path tangential to the curve. If you were on the Tilt-a-Whirl at some sketchy Chinese carnival, and the metal mesh behind you that was supplying the centripetal force keeping you on a curved path was suddenly to vanish (bad rust, let’s say), you would fly off on a path tangential to the curve defined by the edge of the Tilt-a-whirl. If you were lucky, you might land on a plush toy. If you were unlucky, you might land in a malatang or roast squid stall. Poor you. Anyway, the equation, courtesy of Wikipedia, looks like this:
We can ignore the center part. For our purposes force (F) = mass (m) times the velocity squared (v2) divided by the radius of the rotation. In this case, mass is the mass of my son, about 13 kilograms, velocity is (an off-the-cuff estimate) about 1.2 meters per second, and r is about 0.6 meters from the center of rotation to the seat of his pants. So F = 13kg x (1.44 meters per second squared) / .6 meters or 18.72 kg-m-s2 / .6 meters or 31 kg/m/s2. That’s 31 newtons of centripetal force if I’ve canceled the units correctly. But, remember, I nearly failed physics, so this could all be completely wrong. Suffice to say, a distinct degree of centripetal force was required to keep my son from suddenly flying off on a trajectory tangential to the curve.
The centripetal force in this case was supplied by the friction of my son’s jeans-clad rear end on the smooth, vinyl seat of the ice chair. It turns out that there is an equation for this as well. In this case, the equation for static, dry friction, which looks like this (also from Wikipedia):
Where the force of friction (Ff) is less than or equal to the coefficient of friction for the two surfaces involved (mu – the Greek letter that looks like “u” with a hernia) x the “normal” or perpendicular force (Fn), in this case, the weight of my son. The problem I have here is determining the coefficient of friction. It depends on the combination of surfaces involved, and is often looked up on a table that cross-references different kinds of materials likely to be in contact. Despite a thorough search of the Internet, however, I have been unable to locate the coefficient that describes new denim against worn vinyl, which seems like an oversight (hello, Detroit). There’s lots of stuff for metals, plastics, and even leather. But not my exact requirements. Also, there is obviously some deformation of the surfaces involved since neither is entirely rigid, and that would complicate this equation, but is probably unimportant for our purposes.
Anyway, the upshot was that close to the end of the first revolution of the chair, the friction of my son’s rear end on the vinyl seat proved unable to provide the necessary centripetal force to maintain a curved path, static friction became trickier kinetic friction (I don’t even want to go here, mathematically speaking), and eventually no friction, at which point Zachary assumed a ballistic trajectory tangential to the curve, at least until he landed face down on the ice. In fact, the coefficient of friction of just about anything on ice being rather low, he may have continued to slide for some time after impact.
At this point we leave the hard-and-fast world of physics, and enter the much grayer realm of shame. The first thing I did was check for broken teeth, since Zach has already cracked two in the course of regular, boy-like behavior. All teeth were intact, but he had split his lip and lost some skin on the ice. As lip wounds do, it bled copiously.
This being China, there is no shortage of aunties and grandmothers willing to tell anyone, especially foreigners, how miserable their parenting technique is. I have been admonished repeatedly for, among other things, bringing Zach out to the Summer Palace when he was an infant (too young!), dressing him inappropriately (he’ll freeze!) and swinging him around in the courtyard (you’ll pull his little arms out!). My wife has got to the point where she scolds people who provide unsolicited parenting advice. I usually take the more zen “I can’t understand you, I’m smiling and moving on” approach.
In the eyes of Chinese aunties I am sure there is a particularly sweaty corner of hell for people (read: foreigners) who drop their sons face down on the ice. And I could feel dozens of pairs of eyes on me as I slowly poled the chair back to the edge of the lake with my son holding a very bloody tissue to his mouth. This is now one of the three longest journeys of my life. The other two are both aviation-related.
The good news is that Zach had no injury that a cup of hot chocolate and a trip to Hutong Pizza couldn’t cure, and we were back to winter activities last weekend, riding inner tubes down the slope at the Chaoyang Park snow field without incident. But even now I can imagine what those aunties at the lake were thinking to themselves as they watched me bundle a bleeding Zach back to his mom: If he’d studied his physics in high school, this never would have happened.
Note: A little knowledge is obviously a dangerous thing, and it’s possible that the math above is completely wrong in ways I can’t begin to guess. Corrections welcome, but don’t overdo the pedantry. This is, after all, a humor post and not an actual physics lesson. Plus, I’m fragile.