Soccer
Study of the trajectory of a football
Autor:
Título 4
Learning objectives :
This activity allows students to analyze the kinematics of a football shot using a chronophotograph. It develops the ability to graphically interpret the concepts of variable speed and acceleration.
Concepts covered
Projectile movement; Air resistance; Chronophotography; Instant speed; Non-uniform movement
What students will do :
The student uses the FizziQ Kinematic Analysis module to study a chronophotograph of a moving football. After having defined the scale and the time interval between each position, the student successively points to the positions of the ball then analyzes the speed data obtained to determine whether the movement is uniform or not.
What is required :
Smartphone or tablet with the FizziQ application; Chronophotography 'Football' available in the FizziQ library; FizziQ experience notebook
Scientific background :
Chronophotography, a technique invented by Étienne-Jules Marey in the 19th century, allows a movement to be broken down into a series of images taken at regular intervals. It is the direct ancestor of cinema and a powerful tool for cinematic analysis. In this activity, the analysis of a football shot reveals that the movement is not uniform: the speed of the ball gradually decreases. This deceleration is mainly due to air resistance. For a spherical balloon, the aerodynamic drag force can be modeled as: F = ½·ρ·C_D·A·v², where ρ is the air density, C_D the drag coefficient (about 0.2-0.3 for a smooth balloon), A the cross-section of the balloon, and v its speed. This force being proportional to the square of the speed, its effect is particularly marked on powerful shots, where the initial speed can exceed 30 m/s (108 km/h). Additionally, the rotation of the ball (effect) creates a Magnus force perpendicular to the direction of movement and the axis of rotation, which explains the curved trajectories. The FizziQ kinematic analysis module makes it possible to precisely quantify these effects by calculating the instantaneous speed between each position. For a perfectly uniform movement, this speed would be constant. The deviation from this constancy reveals the acceleration (negative in this case), which makes it possible to indirectly estimate the air resistance force and other factors such as the Magnus effect or gravity depending on the components of the movement analyzed.