Tennis Balls and Kinetic Energy

In the first volume of The Feynman Lectures on Physics, Richard Feynman writes, "It is important to realize that in physics today, we no knowledge of what energy is."  Though that quote comes from a book published in 1963, we are in no better position today, nearly a half century later, of knowing what energy actually is.  We use energy concepts all the time to calculate all kinds of wonderful things about nature.  We have all sorts of conceptual ideas of how to understand the application of equations for energy, but, like Feynman wrote, we really don't know what energy is.


Just this morning, I derived the "work-energy theorem" in my Classical Mechanics course, a derivation that always leaves a chill on my spine.  In short, that theorem states that the net work done on an object equals the object's kinetic energy change.  The net work done is independent of the path taken to get from starting point to ending point, and the notion of kinetic energy, or energy of motion, allows for the use of scalars instead of pesky vectors like force and displacement.  The kinetic energy is ½mv², where m is an object's mass and v is its speed measured in some reference frame.  The beauty of the derivation is that kinetic energy is not assumed at the start.  We simply evaluate the work integral for the net force and out pops this thing ½mv² that must be evaluated at the starting and ending points.  Only then do we call that thing "kinetic energy."


While watching yesterday's Australian Open men's final, I saw serves reaching speeds around 110 mph (177 km/hr or 49 m/s).  Given that a tennis ball weighs about two ounces, its mass is therefore about 56.7 grams (or 3.9 millislug, if you really want to use those units!).  Using SI units, a served tennis ball's kinetic energy is thus around 68.5 joules (0.016 nutritional calories or 0.065 Btu or 50.6 ft-lbs).  Of course, the ball's speed goes down on its way to the other side of the court because of air resistance, but something like 70 joules is a reasonable kinetic energy for a professionally-served tennis ball.


Now, think about what speeds some other sports balls would need to have in order to have a kinetic energy of 68.5 joules.  To keep things simple, assume all balls, including our tennis ball, have no spin.  Including spin is not hard, but I'll save a discussion of rotational kinetic energy for another blog post.  A 5-ounce (142 grams) baseball needs to travel 69.6 mph (112 km/hr or 31.1 m/s), whereas a 440-gram (0.97 pounds) Jabulani football needs to travel 39.5 mph (63.5 km/hr or 17.7 m/s).  A teenage boy can throw a baseball 70 mph and a teenage girl can kick a Jabulani football 40 mph.


The lesson here is that some kinetic energies are easier to achieve than others.  Of course, if your technique is good enough to launch a tennis serve at professional speeds, you still have to be able to control it!