We originally wanted to find the relationship between the angle of a tennis racquet on a serve and the distance the ball went. However, upon shooting the video, we realized the video would allow us to find other data. The close-up video was shot at 500 frames/ second, and the full body shot was 250 frames/second. Using Logger Pro 3 and Tracker, we calculated the velocity, acceleration, momentum, and kinetic energy of the racquet at the height of the serve, the speed of the ball immediately after it was hit, the acceleration of the ball, the momentum and kinetic energy of the ball, the rotation of the ball, the force on the ball at the moment of impact, and the velocity of the server's arm during the upward motion of the serve.
Tennis racquet, tennis ball, high speed camera, scale pole, Tracker Program
Mass of objects: Tennis ball 57g and racquet 300g
Velocity, Acceleration, Momentum, and Kinetic Energy of the Racquet
Speed of the Ball
As shown in the table above, the distance the ball is traveling in the x direction keeps increaing, while the distance the ball travels in the y direction decreases with each interval. The velocity of the ball in the x direction is around 1.2 m/s, and the velocity of the ball in the y direction is about -0.1 m/s. The sixth column represents the magnitude of the velocity, which is fluctuating around the 1.2 m/s mark. The third row (2.5s) is clearly when the server strikes the ball since the velocity spikes from 0.5 m/s to 1.168 m/s. The angle from the horizantal at which the ball is traveling is less than 1 degree and is negative, as the ball is traveling downward from gravity.
Acceleration of the Ball
Rotation of the Ball
Momentum and Kinetic Energy of the Ball
Force on the Ball
Comments on Data
There is a precise way the ball, racquet, and arm velocities work during a serve. The racquet speed is around .8m/s and the arm speed is around .6m/s. This velocity allows the ball to hit off the racquet at a speed of 1.2m/s. The racquet is accelerating at about 1m/s/s at the point of contact with the ball, allowing the ball to initially accelerate at 5.022m/s/s. Since the racquet weighs so much more than the ball, the force on the ball is 2.56N mostly in the horizontal direction. The faster the server's arm travels, the faster the ball will go and the higher the ball's initial acceleration will be. The more the racquet weighs, the faster the ball will go and the higher the ball's initial acceleration will be. The more force the ball is struck with, the more momentum and kinetic energy the ball will have. The server who does this with the most accuracy will have the most powerful serve.
THE WAY IT'S SUPPOSED TO BE DONE