Soccer

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.

In the 19th century, French scientist Étienne-Jules Marey invented chronophotography, a technique that captures multiple positions of a moving object on a single photograph at regular time intervals. This revolutionary method, the direct ancestor of modern cinema, revealed for the first time the detailed mechanics of animal and human motion. Today, the same analytical technique is applied in sports science to study the kinematics of every type of athletic movement. When a football is kicked and rolls across the ground, intuition might suggest it moves at a constant speed. In reality, friction with the grass and air resistance continuously decelerate the ball, causing its speed to decrease progressively. This experiment uses FizziQ's kinematic analysis module to study a chronophotograph of a football in motion, measuring successive positions to determine whether the movement is uniform or decelerated, and quantifying the forces at work.

Learning objectives:

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.

Level:

Middle school

FizziQ

Author:

Duration (minutes) :

30

What students will do :

- Analyze a football chronophotograph using FizziQ's kinematic tracking module
- Measure the successive positions of the ball at regular time intervals
- Calculate the instantaneous speed at different points and determine whether the motion is uniform
- Identify the deceleration caused by friction and air resistance
- Understand the difference between uniform and non-uniform motion through quantitative analysis

Scientific concepts:

- Projectile movement
- Air resistance
- Chronophotography
- Instant speed
- Non-uniform movement

Sensors:

- Camera (video/chronophotograph analysis)
- FizziQ Kinematics module (position tracking)

What is required:

- Smartphone or tablet with the FizziQ application
- Chronophotography 'Football' available in the FizziQ library
- FizziQ experience notebook

Experimental procedure:

Open FizziQ and navigate to the Kinematics module. Load the 'Football' chronophotograph from the FizziQ resource library.
Identify the time interval between successive positions in the chronophotograph (this information should be provided with the image).
Set the scale using a known reference in the image (ball diameter = 22 cm, pitch markings, or indicated scale).
Point to the center of the ball at each successive position shown in the chronophotograph. Track all visible positions.
After tracking, examine the position vs. time graph. If the motion were uniform, this should be a straight line.
Note whether the spacing between consecutive positions is constant (uniform motion) or decreasing (decelerating motion).
Calculate the speed between each pair of consecutive positions: v = Δx / Δt.
Plot the speed versus time graph. For decelerating motion, this should show a decreasing trend.
If the deceleration is approximately constant, fit a straight line to the v(t) data. The slope is the deceleration (negative acceleration).
From the deceleration, estimate the friction force on the ball: F = m × a, where m ≈ 0.43 kg for a standard football.
Compare this friction force with the ball's weight (mg ≈ 4.2 N) and calculate the friction coefficient μ = a / g.
Discuss whether air resistance or ground friction is the dominant decelerating force for a rolling ball on grass.

Expected results:

The chronophotograph should show decreasing spacing between consecutive ball positions, clearly indicating non-uniform (decelerating) motion. Initial speeds after a kick typically range from 5-15 m/s, decreasing by about 0.5-2 m/s per second due to rolling friction and air resistance. The speed versus time graph should show a roughly linear decrease for a rolling ball on grass, with a deceleration of 1-3 m/s². The effective friction coefficient for a football on grass is typically 0.2-0.5, depending on grass length and wetness. Air resistance becomes significant only at higher speeds (above 15 m/s for a football), so for moderate-speed rolling, ground friction dominates.

Scientific questions:

- What evidence from the chronophotograph shows that the ball's motion is not uniform?
- What forces cause the ball to decelerate? Which is dominant at low speeds?
- How would the motion differ on a synthetic surface versus natural grass?
- If the motion were truly uniform, what would the position-time and speed-time graphs look like?
- How does the mass of the ball affect the deceleration? Would a heavier ball decelerate more slowly?
- What is chronophotography, and how did it contribute to the development of cinema?

Scientific explanations:

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.

Extension activities:

Frequently asked questions:

Q: The speeds I calculate seem unreasonably high or low. What might be wrong?
R: Check your scale calibration carefully. A small error in the reference distance affects all calculations proportionally. Also verify the time interval between chronophotograph positions.

Q: The speed values fluctuate between consecutive intervals. Is the motion really non-uniform?
R: Some fluctuation is normal due to pointing imprecision. Look at the overall trend rather than individual values. If the trend is clearly decreasing, the motion is non-uniform.

Q: The deceleration is not constant. Is that expected?
R: For a ball decelerating due to air resistance (which is proportional to v²), the deceleration decreases as the ball slows down. Only rolling friction produces a constant deceleration. In practice, both forces act simultaneously.

Q: Why is the friction coefficient for a football on grass so much higher than for ice?
R: Grass is a rough, deformable surface that creates significant resistance to rolling. The ball also deforms the grass blades, absorbing energy. On ice, the surface is smooth and hard, resulting in minimal friction (μ ≈ 0.01-0.05).