Billiards
Conservation of energy: study of collisions between billiard balls
Author:
Title 4
Learning objectives :
This experiment allows students to observe and quantify the conservation of mechanical energy during a collision. It develops their ability to use video analysis to measure physical quantities and to interpret the gaps between theory and practice.
Concepts covered
Conservation of mechanical energy, Elastic and inelastic collision, Kinematic analysis, Kinetic energy, Friction forces and energy dissipation
What students will do :
The student analyzes a video of a collision between two billiard balls using the FizziQ kinematic analysis module. After calibrating the scale, it tracks the position of the balls before and after impact to determine their respective speeds. By calculating the total kinetic energy of the system before and after the collision, it checks whether the mechanical energy is conserved and identifies the factors that could explain possible deviations.
What is required :
Smartphone with the FizziQ application, Billiard ball collision video (FizziQ library or personal video), Experiment book for calculations
Scientific background :
A perfectly elastic collision is characterized by the simultaneous conservation of kinetic energy and momentum. Kinetic energy is calculated by the formula Ec = ½mv², where m is the mass and v is the speed. For a system of two balls, the total kinetic energy before the collision (Ec₁ + Ec₂) should equal that after the collision (Ec₁' + Ec₂'). In reality, even on a professional pool table, a collision is never perfectly elastic. The restitution coefficient (e), defined by the ratio between the relative speed after and before impact, characterizes the elasticity of the shock. For billiard balls, e ≈ 0.92-0.98. Several factors explain the loss of energy: temporary deformation of the balls upon impact, friction with the carpet, air resistance, and transfer of translational kinetic energy into rotational energy. Kinematic analysis by video allows precise measurements to be obtained without complex instruments.