Lighter
Are we lighter on planes?
Author:
Title 4
Learning objectives :
This activity allows students to experimentally verify the variation of the acceleration of gravity with altitude. It concretizes the law of universal gravitation and develops the ability to measure small variations.
Concepts covered
Acceleration of gravity; Law of universal gravitation; Variation with altitude; Gravitational field; Force of gravity
What students will do :
The student compares the value of the acceleration of gravity measured on the ground with that measured at altitude during an airplane flight. Using the FizziQ accelerometer to record the absolute acceleration in the two situations, the student calculates the difference between the two values then compares it with the theoretical variation predicted by the law of universal gravitation.
What is required :
Smartphone with the FizziQ application; A plane flight; FizziQ experience notebook; Calculator
Scientific background :
The acceleration of gravity g varies with altitude according to Newton's law of universal gravitation: g = G×M/r², where G is the gravitational constant (6.67×10⁻¹¹ m³kg⁻¹s⁻²), M the mass of the Earth (5.97×10²⁴ kg), and r the distance from the center of the Earth. At the Earth's surface (r ≈ 6371 km), g is approximately 9.81 m/s². At the cruising altitude of a commercial aircraft (10-12 km), the theoretical reduction in g is approximately 0.003 m/s² (or 0.03% of its ground value). The smartphone's accelerometer measures "absolute acceleration", which corresponds to the standard of the acceleration vector including gravity. At rest on a horizontal surface, it reads approximately 9.81 m/s². This measurement is possible because the sensor detects the reaction force of the support (normal force) which exactly opposes gravity. In horizontal flight at constant speed, the plane is in balance: the lift exactly compensates for the weight. The accelerometer therefore continues to measure "apparent gravity". The decrease in g with altitude is a subtle phenomenon, at the limit of the sensitivity of smartphone accelerometers (±0.01 m/s²). To optimize the measurement, it is recommended to: 1) Take long recordings (>10 seconds) and calculate the average to reduce noise; 2) Ensure that the aircraft is in stable flight (no turbulence or maneuvers); 3) Place the smartphone on a horizontal surface. Even with these precautions, the measurement remains delicate and can be affected by other factors such as aircraft vibrations. This experiment nevertheless illustrates a fundamental principle: gravity is not constant but decreases with altitude, a reality taken into account in calculations of space mechanics and precision geodesy.