General Physics

There are many ways of answering this question. If one were to start at the microscopic level, virtually all of physics could be used! But I'll bet you are really interested in which laws are relevant to an understanding of the game at the level we experience it --- on sizes and time scales relevant to a human player. In that case we're talking what is called "classical physics", or the physics invented by Isaac Newton. His three laws of motion would be the ticket: (1) Any object not acted upon by a force will continue to follow its current motion (either stay still, or continue to move in a straight line with constant speed). (2) When a force acts on a object, the object will accelerate in the direction of the force. The acceleration is proportional to the force (e.g., twice the force, twice the acceleration), and inversely proportional to the mass (amount of matter) of the object (e.g., twice the mass would mean half the acceleration). (3) If an object (call it object 1) exerts a force on another (call it object 2), then object 2 must be simultaneously exerting the same amount of force back on object 1 (an "equal but opposite'' force). Finally, Newton also discovered that gravity is a force describable by the above laws. For our game, the Earth exerts a gravitational force on the ball, players, refs, building, etc., which would accelerate everything downward, except in some cases there is also an upward force, of equal magnitude, keeping the thing stationary (e.g., the player standing on the floor is not accelerating downward because the floor exerts an upward force on his body, balancing the downward gravity force on his body).

Now for some examples of how these laws come into play in basketball. Take a player making a shot. Clearly, if she jumps up from the floor it is because she exerted a force on the floor --- so, by the third law, the floor exerted an equal, but opposite force, on the player, pushing her up! The player then exerts a force on the ball accelerating it out of her hands. Of course, the ball therefore acts back on the player. The result is that the ball, starting from a stop, suddenly takes off with some speed toward the basket. But the player does not take off with an equal speed the other way, because the player is *much more massive* than the ball, so by the second law, the player's acceleration will be much less! The player must be aware (through practice!) that simply accelerating the ball *directly at* the basket will not work --- the ball will end up way below the basket when it arrives. That's because gravity will cause the ball to accelerate downward throughout its flight. The player must actually aim much higher than the basket so the ball will arrive at the basket's height when it finally gets to the basket's vicinity! With that summary of a shot, you can see how each law came into play. Now you can explain any number of other events that occur in the game in a similar fashion, or through other applications of the laws.

Now, this is not a simple question to answer in terms of Newton's laws. Newton can say that the player's weight will imply that the player will not be accelerated much by the force from the ball at the shot, but does that really matter when it comes to *making baskets consistently*? I doubt it, since practice would enable the less massive player to know (intuitively) exactly how to compensate for any troubling effect. Similarly, height may not matter. However, in a real game, it's not simply what you (the shot maker) is like, but what the defenders are like as well! I'm sure a taller player will have an advantage over a shorter player when it comes to shooting the ball over tall defenders! Weight may also be a factor in the tight spots (where you have to fight for a shot). These factors are not simply ranked from the point of view of the fundamental physics. (Maybe that's why you need to know more than physics to play basketball!).

The physics of dance would also be the classical, Newtonian, physics. But I think the situation is probably even more complicated than in basketball. Sure enough, jumping from the floor means pushing down on the floor (so the floor pushes back equally), but a dancer needs to be graceful, and in control of her body's appearance and muscles throughout all the actions, even when off the floor. For example, producing certain positions of limbs with respect to other parts of the body, and changing those orientations *while off the floor* (at times), means moving one limb, and correcting for the "equal but opposite" reaction of the adjoining part. It's very difficult to see how (or calculate how) all these interacting parts need to be moved simultaneously to produce the desired effect. However, as in the basketball situation, practice is how the mind determines what to do (and therefore builds up the intuition for how to handle each new situation).

There is one thing that occurs in both dance and basketball that aficionados recognize as special: the person who seems to be able to "hang in the air" for a long time during a jump. Unless the person has wings (or is wearing a sail, etc.), there is, of course, no way any specific individual can hang in the air longer than anyone else, unless they jump higher. The acceleration of gravity is the same for everyone, regardless of their athletic ability, or mass, or anything else. HOWEVER, some can appear to jump higher, or appear to stay higher for longer than others by using their bodies in a special way. The explanation goes as follows: The "center of mass" of your body must follow the same type of path through space during a jump as for any other person --- it is a "parabolic" path (ask your teacher about what the path looks like). The center of mass point of your body is the balance point --- if you stretched horizontally across the top edge of a roof (the peak), you'd have to position your center of mass directly over the peak to avoid tipping over to one side of the roof or the other. Now, although your center of mass has to follow a parabolic path, you can adjust the parts of your body, during the flight, to cause arms and legs, etc., to be going up, or staying at the same height, while the center of mass is falling down! The result: it looks like you're hanging in the air for a bit of time. Of course, once again, it's through practice that dancers accomplish this, not through a study of physics (but it is interesting to understand, through physics, what they are doing, and what limitations exist).

I congratulate you on your initiative and curiosity! You may learn a great deal on your own through your investigations.

Your question (about what forces to include in your program, and how) has no good answer --- if you mean to include every force possible and every sort of particle. We don't yet know everything! Even in a practical sense it would be nearly impossible to include all we do currently know in one such program which would then yield useful information; certainly it would not be the "simplest of programs."

No scientist tries to work that way. Instead, one concentrates one's efforts on a small piece of the puzzle --- usually that's difficult enough. Nevertheless, it is possible for you to write a program to follow the motions of 1000 particles interacting in a reasonable fashion. I suggest you concentrate only on a Newtonian gravitational interaction. You will be able to accomplish this task, and probably learn a great deal in the process. Besides, after the very earliest moments of the Big Bang, gravity is the most important force in deciding the future evolution of the universe.

Each particle can be assumed to have the same mass (for simplicity!). For a particle of mass m (particle A) experiencing the gravitational force of another particle (particle B, also mass m), the force on A is toward B and of the amount Gmm/r^2 where "r^2" you might recognize to be "r squared." G is Newton's gravitational constant. Each particle A in your collection will experience a force from *each* other particle --- these individual forces add up as vectors to give the total force F acting on A.

Then, particle A therefore has an acceleration a=F/m due to the total force F acting on it Now, your program must follow the motion of each particle under the influence of the force F acting on it. This is simple in principle, but can be complicated in practice.

From reading your message it is clear you might want to get much more information than I can give you through e-mail messages. You should probably consult some introductory textbook on physics to fill in the details of what I said above. Might I suggest The Feynmann Lectures on Physics by Richard Feynman. Chapter 9 in volume 1 discuss the above calculations in basic detail. You might also benefit from looking at some similar programs. The collection of BASIC programs presented in Sky and Telescope magazine might be interesting. You can see them all by going to Sky and Telescope's website at http://www.skypub.com. Good luck.