Basketball
Jeff Peck & Catherine Lewis
Basketball
There are many aspects and skills involved in the game of basketball:
Dribbling Cutting (changing direction) Passing
Dribbling
An elastic collision is preferred Deflated ball loses energy to the floor Better inflated ball will lose less energy because not as deformed by floor Greater conservation of energy allows more predictable bounce
Changing Direction
Need traction between floor and shoes
μ must be large Static friction should be considerable
Passing
F=ma=m(v/t) Increasing time lessens force When receiving a pass: putting slightly bent arms out allows hands to decelerate ball over greater amount of time, thus decreasing force on chest
Shooting
This is perhaps the best-known skill An individual can be sub-par in every other aspect of the game, but if they can shoot well they become a prized asset of any team. In addition, essentially all super stars are known for there scoring ability
The Free-Throw
There are several factors that are integrally involved in the shot
Angle of release Initial velocity Acceleration Force (by player and gravity) Mass
We will not take into account the minimal air resistance
How does this happen?
First, we will look at the most basic shot: The free-throw
Though simple, this shot can often be the difference in a game
There is no jumping, driving, or any other extraneous movement to take into account
Statistics on Free Throw Shooting
x=4.57m y=1.32m (above head) Avg. Time=1.065sec Y=V0yt-1/2gt2 X=V0xt V0y=6.46m/s V0x=4.29m/s tanθ=Y/X=6.46/4.29=56.41° V0=(6.46m/s2+4.29m/s2)1/2=7.75m/s VY=V0Y-gt= -3.98m/s At basket: V= (3.98m/s2 + 4.29m/s2)1/2= 5.85m/s Maximum Position: 0=6.46m/s-gt t=.659s Y=V0Yt-1/2gt2=2.13m (above head)
X=V0xt=2.83m
Conservation of Energy: h1=1.77m h2=1.77m + 2.13m=3.91m h3=3.05m V1=7.75m/s V2=4.29m/s V3=5.85m/s
K1 + U1 = K2 + U2 = K3 + U3 1/2mv12 + mgh1 = 1/2mv22 + mgh2 = 1/2mv32 + mgh3 ½(7.75m/s)2 + g(1.77m)= ½ (4.29m/s)2+g(3.91m)= ½ (5.85)2 + g(3.05m) 47.38J = 47.52J = 47.00 J
Spin
Players shoot with backspin on the ball Unlike baseball, velocity is too small for spin to affect air resistance When ball hits the rim or backboard, it will bounce off in the opposite direction in a vertical path toward net Backspin gives a greater chance of shot going in if it hits anything Spin helps shooter develop muscle memory so they can reproduce the same shot repeatedly
Jump shot
Now we will explore a more difficult shot: the jump shot
Jump Shot
This shot includes all the variables from the Free Throw in addition to a few new aspects
The height off the floor Lateral movement Velocity of body at time of release
Jump Shot
This makes the Jump Shot much more difficult In order to eliminate as many variables as possible in their shots, players attempt to jump to the same height, release at the same time, and not drift to either side while shooting
The great players can often make shots with these additional variables. However, a good shooter will try to make the shot as easy as possible to enhance the likelihood of making the shot.
Sources
http://www.u.arizona.edu/~clc1/lab3/lab3.ht ml www.geocities.com/thesciencefiles/physics of/basketball.html www.hesston.edu/academics/faculty/nelson k/physicsResearch/basketball/Mainpage.ht m-3k