Huygens
Conservation of energy for a pendulum (kinematic study)
Author:
Title 4
Learning objectives :
This activity allows students to experimentally verify the principle of conservation of mechanical energy for a pendulum. It develops the ability to analyze an oscillatory movement and to quantify energy transformations.
Concepts covered
Conservation of mechanical energy; Simple pendulum; Potential and kinetic energy; Analysis of oscillatory movement; Harmonic motion equations
What students will do :
The student uses the FizziQ Kinematic Analysis module to study the movement of a pendulum. By pointing out the position of the ball during its descent and analyzing the position and speed data, the student calculates the potential energy and the kinetic energy at different moments of the movement then verifies that their sum remains constant.
What is required :
Smartphone or tablet with the FizziQ application; 'Pendulum' video from the FizziQ library or personal video of a simple pendulum; Optional: spreadsheet for energy calculations; FizziQ experience notebook
Scientific background :
Christiaan Huygens (1629-1695), a Dutch scientist, developed the pendulum theory and invented the first accurate pendulum clock. The analysis of pendulum movement perfectly illustrates the principle of conservation of mechanical energy later formulated by Leibniz. For a simple pendulum, this energy breaks down into two forms: gravitational potential energy, Ep = mgh (where h is the height relative to the lowest point), and kinetic energy, Ec = ½mv² (where v is the instantaneous speed). According to the conservation principle, the sum Ep + Ec remains constant in the absence of friction. At the highest point of motion, the energy is mainly potential (v ≈ 0); at the lowest point it is mainly kinetic (h = 0). Between these extrema, energy gradually transforms from one form to another. The FizziQ kinematic analysis module makes it possible to precisely quantify these transformations by providing the y coordinates (to calculate h) and the speed v at each instant. For an ideal frictionless pendulum, the total mechanical energy should remain perfectly constant. In practice, there is a slight decrease over time, mainly due to air resistance and friction at the suspension point. This decrease is an example of energy dissipation, converted into heat according to the second law of thermodynamics. The amplitude of the oscillations thus gradually decreases, a phenomenon called damping. The rate of this decrease can be used to estimate the coefficient of friction of the system.