Newton's pendulum
Newton's pendulum and elastic shock
Author:
Title 4
Learning objectives :
This activity allows students to verify the conservation of mechanical energy during collisions between the balls of a Newton's pendulum. It develops the ability to analyze energy transfers and understand conservation concepts.
Concepts covered
Energy conservation; Elastic and inelastic collision; Energy transfer; Restitution coefficient; Shock dynamics
What students will do :
The student uses the FizziQ kinematic analysis module to study the movement of the balls of a Newton's pendulum before and after impact. By measuring the position and speed of the balls at different times, the student calculates the kinetic and potential energy of the system then compares the values before and after collision to check if the total mechanical energy is conserved.
What is required :
Smartphone with the FizziQ application; Video 'Newton's Pendulum' available in FizziQ resources; FizziQ experience notebook
Scientific background :
Newton's pendulum, named after Isaac Newton although he was not its inventor, is a device that perfectly illustrates the principles of conservation of momentum and mechanical energy. It usually consists of five identical metal balls suspended side by side. When you move a ball aside and release it, it hits the others and, surprisingly, only the ball at the opposite end rises, and to the same height as the first. Physically, two principles are at work: 1) The conservation of momentum: mv₁ = mv₂ (where m is the mass of the balls and v₁, v₂ the velocities before and after collision); 2) Conservation of mechanical energy: ½mv₁² = ½mv₂² (neglecting losses). For a perfectly elastic shock, these two laws impose that in a system of two identical masses, all of the kinetic energy is transferred from the first mass to the second. In a real pendulum, shocks are never perfectly elastic: part of the energy is converted into heat, vibrations or sound waves. The restitution coefficient e characterizes this loss of energy: e = √(E₂/E₁), where E₁ and E₂ are the mechanical energies before and after collision. For a perfectly elastic shock, e = 1; for a totally inelastic shock, e = 0. The kinematic analysis of FizziQ makes it possible to precisely measure the energies at different times and to calculate this coefficient. Commercial Newton pendulums typically have a coefficient e between 0.9 and 0.95. This experiment provides a visual understanding of abstract concepts such as conservation of energy and momentum, and illustrates the difference between theoretical models (perfect conservation) and physical reality (inevitable losses).