physicsoftennis

Tennis Anyone?

"The Physics of Tennis"
BY

Matt Jochmans Aashish Shah Mike Davison

This page is an honors project for our Michigan State University Physics class (LBS 164). This page deals with the concepts of Physics concerned with the great gentlemen's (and gentlewomen's) game of Tennis. We will be addressing the complexity behind the topspin shot and effects of string tension upon performance.

For this, we must take an in-depth look into the realm of Physics and explore (I)Conservation of Momentum, (II)Rotational Momentum, (III)Kinematics in Two Dimensions, and (IV) Newton's Laws.

Topspin

Topspin is one of the most difficult, yet effective shots in the game of Tennis. It is when a player hits the ball in such a way that the ball spins clockwise upwards, and then quickly falls to the ground before the opponent can react. Contrary to popular belief, topspin shots are used in more instances than just lobs. In the hands of an expert, the topspin shot is deadly. But how does this shot occur?

It occurs due to a few underlying laws of Physics. Since the collision between the ball and the racket is inelastic, because the ball does not stick to the racket, and kinetic energy is lost in the collision, we can use the following concepts to explain the phenomena of a topspin shot:

(I) CONSERVATION OF MOMENTUM:
This law states that the momentum (which is just the mass times the velocity) before a collision occurs, is equal to the momentum after that particular collision. This is definitely the case in tennis. The momentum of the tennis ball and the racket before they collide together is equal to the momentum of the ball and the racket after. So, the equation is as follows:

(Mass of ball*velocity of ball)+(mass of racket*velocity of racket)=(mass of ball*velocity of ball after collision)+(mass of racket*velocity of racket after collision)

This equation indirectly influences the topspin shot by allowing rotational momentum to exist during the trajectory of the topspin shot.

(II) ROTATIONAL MOMENTUM:

This concept is the main reason why topspin is different from all other tennis strokes. The fact that topspin shots rotate the ball while in it's trajectory, gives the tennis ball another factor in calculating it's velocity and position. What occurs is that the ball's rotation makes the ball spin, which gives it an additional velocity vector. This new velocity vector, called Angular Velocity, must be added to the linear velocity in order to calculate the true speed of the ball. Angular Velocity is equal to the linear speed divided by the radius of the tennis ball, and is also equal to the total number of rotations completed divided by the time in motion. We can calculate this new velocity vector in the next section, kinematics.

(III) KINEMATICS:

When the racket comes in contact with the tennis ball, it exerts a force upon that ball, which propels the ball forward. However, this force upon the ball is in two dimensions, which we call X and Y. This is true because the racket should never be perfectly parallel when hitting a topspin shot. The fact that the racket is being swung at an angle other than 90 degrees, makes the following statements true:
The force in the X direction is equal to the total force times cos of theta (Fx=F cos theta)
The force in the Y direction is equal to the total force times sin of theta (Fy=F sin theta)

The fact that a force in the X direction exists gives the topspin shot it's spin. Since the fact that in order to hit a topspin shot you have to basically move your tennis racket upwards while in contact with the ball gives the ball a lot of force in the up (Y) direction. This is the reason why topspin shots normally go up further and have higher trajectories.

(IV) NEWTON'S 3 LAWS OF MOTION:

The game of Tennis is based upon Newton's Laws. These laws serve as a basis for our understanding of the topspin shot.
Newton's 1st Law states that a body in motion tends to stay in motion, and a body at rest tends to stay at rest. The ball would not be able to travel across the court without this law.
Newton's 2nd Law states that force is equal to mass times acceleration. We used this definition of force in the Kinematics section.
Newton's 3rd Law states that every action has an equal but opposite reaction. The tennis ball would never bounce off the strings of the racket and travel over the net if this law did not exist.

Without these laws, there would be no physical way to play the game of tennis.

SOME OTHER IMPORTANT AND INTERESTING FACTS:
Next time you go to string your rackets, keep this in mind: When asked what tension you would like your racket strung at, think about your style of play. Do you require more control and consistency when on the court? Then, string your rackets at about 63 to 70 lbs, a higher tension than normal. If you require generating much more power, then experiment with stringing your racket at 53 to 60 lbs, a lower tension than normal. Why??????????????????????????????

Well, to start with, when the racket makes contact with the tennis ball, the strings actually give a little in the opposite direction of the tennis stroke. This is vital, because this gives the tennis ball it's momentum (as explained above). Thus, when the tension of the strings is lower, the strings tend to give way a little more, and due to the conservation of momentum theory, the ball is then projected over the net at a greater speed. This is because the tennis ball, during the small time span when it actually makes the strings bend (so the stings have a higher tension during that brief time) gets additional amounts of speed from the tension of the strings acting on the ball. This is in addition to the speed from the act of being inelastically bounced off the racket.

Conversely, if the strings are higher in tension, the strings will give much less, therefore reducing the speed of the ball, but alternately giving the tennis player much more control over his or her stroke. If the aforementioned seems confusing, an easy comparison can be made to that of a slingshot.

When you pull the rubber band back a little, but not all the way back, the buckeye (or whatever you are using for ammo, I preferred buckeyes back in 5th grade), does not travel as far as if you pulled it back all the way, but you now acquire better accuracy. This is directly related to when the tension of strings in tennis rackets are high.

However, if your target is across the backyard, you want increased speed over accuracy. Therefore, you pull the rubber band as far back as you can. This is exactly the effect that occurs when strings in tennis racket are at low tensions.