Rafael Nadal and Newton's Third Law

I caught a glimpse of Rafael Nadal's opening match against Alex Kuznetsov.  The world's #2-ranked men's tennis player easily dispatched Kuznetsov in straight sets, thus kicking off Nadal's efforts to win a second Australian Open.


Newton's laws have been on my mind of late, and watching a tennis ball in flight brought the third law to the front of my mind.  One must employ Newton's second law if one wishes to model the trajectory of a tennis ball in flight.  Instead of thinking about that, I thought of the remarkable subtleties in Newton's third law.  Two objects exert forces on each other of equal magnitudes and opposite directions.  Some refer to this idea as "action/reaction," but I can't stand those terms.  When I hear "action/reaction," I think that one force is the "action," and then the other force comes along a little later as the "reaction."  That's not what happens!  One object exerts a force on another object at exactly the same time as the second object exerts a force on the first object.  One force does not precede the other.


The third law also tells us that forces, much like the Sith in Star Wars, come only in pairs.  There is no such thing as an isolated force.  Because the idea of a force requires two objects, Newton's third law pairs never appear on the same object.  Think about Nadal's powerful serve.  After the ball leaves his racket, and before it reaches the court's surface on the other side of the net, there are two forces on the ball.  One comes from the air (drag, Magnus, and buoyant forces are all air forces); the other comes from the Earth (gravity).  The third-law pair to the former force is a force on the air from the ball; the third-law pair to the latter force is a force on the Earth from the ball.  Think about that.  The ball exerts a force on the Earth of exactly the same magnitude that the Earth exerts a force on the ball!  Further, the ball pulls the Earth up while the Earth pulls the ball down.  That's true whether the ball is in flight or in Nadal's pocket.  Many people new to physics often have trouble with this idea.  Take the tennis ball's mass to be 58 grams.  That's a tad more than 2 ounces or almost 0.57 newtons.


So, do you believe that a tennis ball pulls up on the Earth with 2 ounces or 0.57 newtons of force?  To believe it, one may need to think about Newton's second law.  Sure, the tennis ball and Earth exert equal and opposite forces on each other, but we see only the effect of the Earth's force on the ball.  We don't see the Earth move!  That's because the Earth has a mass that is 100 trillion trillion times that of a tennis ball.  Drop a tennis ball, and it accelerates to the ground at about 9.8 meters per second per second (that's about 22 mph each second).  That acceleration is due to the Earth pulling on the ball with 2 ounces or 0.57 newtons of force.  The Earth hardly notices that same magnitude of force on it from the ball.  It's upward acceleration is 100 trillion trillion times smaller than that of the tennis ball.  Drop a tennis ball from a height of about 1 meter (a little more than 3 feet).  It takes about 0.45 seconds for the ball to hit the ground.  In that time, the Earth moves only about one trillion trillionth of a centimeter, which is 16 orders of magnitude smaller than the width of a hydrogen atom!  Suffice to say, the Earth couldn't care less that a tennis ball is pulling on it with 2 ounces of force!