Physics of Tennis
Updated: Thursday, August 16, 2018 9:48 AM
Tennis is an exciting sport, and the rally is the most fundamental part of this game. During a rally, the opponent successively hit the ball with their tennis racquets back and forth across the net until a player makes a mistake. There is a remarkable display of fundamental mechanical principles in motion governing the ball or trajectory. The same fundamental mechanical principles we studied in Basic physic is what governs the dynamics of motion of a tennis ball. It is impossible to easily derive an equation for the flight path of tennis ball once a racquet hits it due to the sheer number of force interactions that take place. However, we will discuss briefly some of the physical principles that govern the movement of the tennis ball. How I came up with tihs idea? It's simple! I just always loved tennis and had problems with college physics. So I started learning physics with MC2 and here you have a result of my work, enjoy!

## Newton’s Laws of Motion

Newton’s laws of motion are the fundamental physical principles that govern how objects move, including the tennis ball. There are numerous ways Newton’s law of motion applies to how the tennis ball moves; however, only a few will be listed in this article. Newton’s second law of motion describes what happens whenever the tennis racquet comes in contact with a ball; this law shows the relationship between external force on the object to the resulting acceleration of the object, determines the resulting acceleration of the ball due to the effect of the racquet on the ball. Also, Newton’s third law reveals that the force exerted by the tennis ball on the racquet is equivalent in magnitude and opposite in direction to the force exerted on the tennis racquet by the ball.

## Gravity

Gravity makes it possible to place tennis, if there is no gravity, after hitting the ball, it won’t come down and bounce in the court. A tennis call undergoes an acceleration due to gravity continually. Gravitational force acts downwards on the ball; this force is perpendicular to the surface of the court. The equation below shows the relationship between the magnitude of the gravitational force on the tennis ball.

F_g=mg

m= mass of the ball, which by regulation is approximately 57g

g= acceleration due to gravity close to the earth’s surface, g= 9.81

## Impulse and Momentum

When hitting a tennis ball with a tennis racquet, the racquet’s force on the tennis ball delivers an impulse to the ball while the ball and the racquet are in contact. The racquet’s force magnitude on the tennis ball varies with time, the force is low at initial contact, and reaches maximum when the racquet string deformity and the ball compression reaches a maximum, before reducing back to zero as the tennis ball leaves the racquet string. According to the impulse-momentum theorem,

\vecJ=\vecp_f-\vecp_i=\Delta \vecp

J is the impulse on the ball

P is the momentum of the ball.

Impulse on the ball = change in momentum of the ball

## Collision Elasticity

The strings of a tennis racquet are very elastic; thus, exert a strong restoring force on the ball when it comes in contact with the string, this adds to the impulse transferred to the tennis ball when the racquet hits it. Comparing the strings of a tennis racquet to a tennis ball, the ball is relatively inelastic. Therefore, a tennis ball loses energy to dissipative forces as they bounce because of friction that exists between the ball and the court as well as the tennis ball deforming. To quantify the elasticity of an object (e.g. tennis ball), you need to measure the object’s coefficient of restitution on a surface (tennis court).