![[Virginia Tech Department of Physics]](vtlogo.gif)
Back to Frequently Asked Astronomy and Physics Questions
Which laws of physics pertain specifically to basketball?
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.
What components of Newtons laws of motion are most important to
shooting and making a basket?
See above answer!
Do the same forces act on the ball that act on the person shooting?
Yes!... but in the opposite direction. See answer to question 1.
Is a player's height or weight more critical in terms of jumping and
shooting?
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!).
I am interested in the physics of
dance and movement. Would the same laws of physics also apply to those
types of things?
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).
One hobby of mine is programming. I am currently trying to create a
virtual universe. What forces do I need to take into account? Of course, It won't be quite as big or as fast as the
real thing. I want to create about 1000 of the most basic particles known
to man in a virtual universe. The way it is set up is each particle has an
x,y,z coordinate x,y,z velocity, and mass. What I want to know is how they
interact. What different forces bind them? And how? Perhaps I can simulate
the big bang with the simplest of programs.
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.
I have two same caliber projectiles, both weighing the same. If
one is fired out of a gun at 2000 fps and the other one is dropped free at
the exact same time and height as the gun, would they both hit the ground at
the same time?
A different variation of the question would state: If two projectiles, both
same in diameter and configuration but of different weights, were fired at
the same time and at the same velocity, would they both hit the ground at the
same time?
In answer to your questions: It depends!
If you assume no air resistance (or if the experiment is done in a vacuum), then the answer will not depend upon the weight of the objects in question (or any other attribute of them, such as shape).
In vacuum, if the projectile fired out of the gun is fired along a line parallel to the ground, then both projectiles will hit the ground at the same time, regardless of the velocity of the fired projectile.
Actually, there is another level of complexity that could be taken into account: both will hit the ground at the same time only if the Earth's curvature can be ignored! If the fired projective is moving fast enough (or from a high enough height) to proceed far enough toward (or past) the horizon before it hits the ground, then the fired projectile will hit the ground later than the dropped projectile. (At a truly very fast speed of firing, the projectile may never land, simply falling along a curve that never reaches the surface of the curving Earth. Then the projectile would be in orbit. That's what the Space Shuttle is doing.)
If the experiment is done in air, then the shape and weight of the projectiles would matter to some extent. For instance, a projectile of large density would fall to Earth quicker than one of the same weight but lower density (larger volume). To take an extreme example, a feather weighing the same as a penny would obviously fall slowly to Earth compared to the penny.
