Basketball was invented by James Naismith in 1891. He had a particularly rambunctious group of young men to deal with that winter and found most indoor sports were too violent. He conceived of a game of passing and shooting with no physical contact. The object was to get the ball into a peach basket mounted on the balcony of the gymnasium.
Basketball has come a long way since those early days. Players dribble the ball down the court. Lay-ups and slam dunks dominate shooting unless it is a three pointer. And physical contact abounds, particularly when men play.
But the basket is still the same ten feet off the floor.
In many ways, the game is fairly simple. The science behind the game is not. The number of calculations going on inside LeBron James's mind as he goes in for a lay-up or in Stephen Curry's head as he pulls up for a three pointer is astounding. They are intuitively solving a half a dozen trigonometric and calculus equations at once. Fortunately, they can do this subconsciously and in a split second otherwise the game would be rather tedious.
Consider just one part of the game - the slam dunk. The angle of takeoff, the distance from the hoop, the timing of the leap, the force involved, and the positioning of the ball all need to be worked out.
A good player can jump up to four feet vertically and 15 feet horizontally. But the trick is for the apex of the jump to occur in such a way as to allow the player to stuff the ball through the basket. All of the critical decisions must be made prior to take off because once the player is in the air, they can do very little to affect their flight.
An effective jump requires a lot of friction between the foot and the floor. At the point of departure, the player's foot is pushing both down and backwards. The downward force is required to overcome the effects of gravity and provide the four feet of height. The backwards force provides the distance.
Newton's Third Law comes into play: "for every action, there is an equal and opposite reaction." The force the player uses against the floor must be equally balanced by the force the floor applies to the player. This energy goes into the jump. Without friction between the foot and the floor, the force wouldn't be balanced and the player would fall.
During the dunk, basketball players often seem to float through the air on their way to the basket. It is a bit of an illusion but has a lot to do with the structure or physics of a jump.
We all know gravity is pulling us down. When jumping, we are momentarily overcoming the forces of gravity by accelerating in the opposite direction. As we climb, our vertical speed decreases until we hit the apex of our jump and then we begin accelerating in the opposite direction.
What this looks like is a very fast takeoff speed which decreases to zero over a short period of time and then we slowly begin to accelerate towards the floor once more. The equations for gravity from high school physics can be used to analyze the flight. They tell us almost three quarters of our flight time will be spent in the upper half of the jump.
Further, it is our centre of mass which follows the parabolic arc describing the jump. This is not constant. As our arms move the ball to bring it into position, it slightly decreases the height of our centre of mass initially and elevates it as the ball is slammed home. The resulting jump is not a perfect parabola. It is flattened in such a way as to give the appearance of more sustained horizontal flight. Hence, the physics of the jump leads to the illusion of sustained flight.
To actually dunk a basketball, it needs to travel through the hoop. This means it is not sufficient to simply arrive at the rim. The ball must pass over the top and then be propelled downward through the hoop. Again, Newton's third law tells us the force applied to push the ball down is balanced by the force of the ball on the hands.
Finally, at the end of the jump, the player lands. The floor applies force to the feet and the body. How much? Exactly the same amount the player used to jump in the first place. The forces are symmetrical. And, of course, friction comes into play as it allows the player to stop and not slide.
This is the simplified version of the science in just one part of the game of basketball which involves angular momentum, leverage, biophysics, biochemistry and a whole lot more.
Go, Timberwolves, go!
