Estimation of g by kinematic study
Determining the acceleration of gravity by video analysis
Author:
Title 4
Learning objectives :
This activity allows students to experimentally determine the value of the acceleration of gravity by video analysis. It concretizes the equation of parabolic motion using digital modeling tools.
Concepts covered
Parabolic movement; Acceleration of gravity; Equations of motion; Data interpolation; Kinematic analysis
What students will do :
The student analyzes the parabolic trajectory of a ball using the FizziQ Kinematics module. After calibrating the scale of the video and pointing out the position of the ball on each image the student uses two complementary methods to determine g: first by analyzing the slope of the vertical velocity curve then by examining the coefficient of the quadratic term in the position equation.
What is required :
Smartphone or tablet with the FizziQ application; 'Parable' video from the FizziQ library or personal video of an object in free fall; FizziQ experience notebook
Scientific background :
An object moving in the Earth's gravity field experiences a constant acceleration g ≈ 9.81 m/s² directed vertically downwards. This acceleration only affects the vertical component of the movement, the horizontal component remaining uniform in the absence of friction. For vertical motion, the time equations are: y(t) = y₀ + v₀ₜt - ½gt² and v_y(t) = v₀ - gt. FizziQ's kinematic analysis tool allows you to experimentally verify these equations by tracking the position of an object frame by frame. Two methods of estimating g are possible: 1) From the speed: v_y being a linear function of time, the slope of this line corresponds to -g. Linear interpolation provides this value directly. 2) From the position: y(t) being a quadratic function, the coefficient of the term t² is worth -g/2 in the interpolation y = at² + bt + c. Sources of error include: pointing inaccuracy, perspective effects if the camera is not perpendicular to the plane of motion, and the influence of air resistance which can slightly reduce the effective acceleration. The use of two independent methods makes it possible to validate the consistency of the results. This experiment perfectly illustrates the universality of the law of gravitation: all bodies fall with the same acceleration regardless of their mass, a principle discovered by Galileo in the 17th century.