Physics Of Tennis

The sport of tennis has multiple opportunities in which the study of physics can go in depth. The sport’s court, racquet, ball, and even the player contain unlimited amounts of physics in which a person can go more into detail with as they study. While it is true that these all contain some form of physics, the racquet and how it interacts with the ball is where most of the physics is apparent. Starting with the racquet a person is able to see four main areas of focus. These focuses consist of the racquets sweet spot, vibration nodes, center of percussion, and the dead spot of the racquet. As a person goes farther into researching each individual subject, they learn that the sweet spot is located near the center of the strings (Brody, 1981).
While most people believe that the sweet spot allows the player to hit the ball with the maximum amount of speed, they are mistaken; the sweet spot merely prevents the player from causing jarring to occur to the wrist (Brody, 1981). Going on with the physics of the racquet a person would go onto the next focus being the vibration nodes. The racquet compares with a uniform beam, despite its large round head, due to the center of mass being near the center of the racquet (Brody, 1979). Some racquets fundamental mode contains an estimated frequency of 100 Hz to allow its frame to be relatively flexible, while others contain an estimated 180 Hz for a stiff frame (Brody, 1979). The racquet as a whole contains two different vibration nodes, one located near the center of the strings and the other located in the handle (Brody, 1979). Vibrations are sent within the racquets frame as the ball makes contact with the racquet; to dampen these vibrations one can grip the handle tighter, or apply a piece of rubber towards the bottom of the strings. Another node that creates the uniformed beam has a frequency 2.75 times that of the fundamental frequency (Brody, 1979). This does not cause any significant amplitude since the impact duration of the ball as it makes contact with the string is about five m/s (Brody, 1979). The frequency spectrum of this pulse is approximately a half sine waveform causing it to peak at zero frequency, which is at f= 1.5/T= 300 Hz, which causes it to excite string vibration of 500 Hz, since frame is more dampened than the strings (Brody, 1979). The next area of the racquet would be the center of percussion; this is the impact point in which the force a person’s hand hits the racquet as they swing through the ball.
However, the center of percussion is not at the exact spot in which the hand meets the racquet due to the hand adding an additional mass of about 500 grams, which in turn causes the location to shift to a position near the throat area of the racquet (Brody, 1981). Due to the force of the hand being at zero for the impact at the center of percussion, it is often considered to be the second sweet spot (Brody,
1981). As a person continues learning of the physics of the racquet, they learn about the dead spot of it. As a person hits the ball with their racquet, they can quickly learn how the ball bounces back best near the throat of the racquet, while it is near the tip of the racquet that the ball does not bounce at all (Brody, 1979). This spot at the top of the racquet is the dead spot. At this location, all of the energy from the ball is given to the racquet, while none of the energy is given back, the reasoning behind this is that the effective mass of the racquet near this location is equal to the mass of the ball (Brody, 1979). This effective mass is the ratio of the force at that point to the acceleration of that particular point, using the formulas F=ma so m=F/a. It is the as if the mass of a ball were to collide with another ball of the same mass at rest, the ball in motion would stop dead while the ball in rest would absorb the others energy (Brody, 1979). After studying all a person can basically study about the physics of a tennis racquet, it would be a reasonable idea to move on to the physics of a tennis ball.
Using study it has been scientifically proven that a tennis ball will bounce to a height between fifty-three and fifty-eight inches when dropped from a height of one-hundred inches with no force added onto a level slab of concrete (Howard, 1987). However, knowing this information does nothing to predict how the ball will bounce as the game is played out. As a tennis ball bounces on the ground 45% of its energy is lost, while it only losses an estimated 30% of its energy when hit against the string of a racquet. This is because the strings are formed in a way to absorb the energy of the ball and then return the energy back as the ball pushes off (Howard,
1987). A major part of the game of tennis is the amount of spin a player can apply to the ball. Topspin will allow the player to hit the ball harder, while still allowing it to fall in; while backspin stops the ball from moving forward after the first bounce. The amount of spin applied to the ball includes multiple factors including the speed of the ball, the angle at which the ball hits the racquet as well as the ground, the type of strings, and the size of the racquet head. As a person relates how these two objects work together in physics to form the game of tennis, it becomes easier for the people to notice how often physics is at work even when it is not apparent. Physics can be found it almost everything going on within this world, if a person would just step back and let themselves see what is really going on around them.