14.6
Accélération due à la gravité sur Terre
Selon la loi de gravitation de Newton, la force gravitationnelle exercée sur un corps est proportionnelle à sa masse. Selon la deuxième loi du mouveme…
Un objet est considéré comme en chute libre lorsque la seule force agissant sur lui est la force gravitationnelle de la Terre. L’accélération d’un tel objet en chute libre est appelée accélération due à la gravité, notée g.
Selon la deuxième loi du mouvement de Newton, l'intensité de la force agissant sur l'objet est égale à sa masse multipliée par son accélération. Il est également connu sous le nom de poids de l'objet.
En équivalant à mg à l'équation de la force gravitationnelle, l'accélération due à la gravité de l'objet peut être exprimée comme le produit de la constante gravitationnelle et de la masse de la Terre, divisé par le carré de sa distance au centre de la Terre.
La valeur moyenne mesurée de g près de la surface de la Terre est de 9,8 m/s2. Comme g est indépendant de la masse de l'objet, toutes les masses proches de la surface de la Terre tombent en chute libre avec la même accélération.
Par conséquent, en substituant les valeurs de l'accélération due à la gravité, de la constante gravitationnelle et de la distance comme rayon de la Terre, la masse de la Terre est estimée à 5,97 × 1024 kilogrammes.
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Q1: What is acceleration due to gravity and how is it defined?
Acceleration due to gravity, denoted by g, is the acceleration of an object when only Earth's gravitational force acts on it during free-fall. According to Newton's second law, this acceleration equals the gravitational constant multiplied by Earth's mass, divided by the square of the distance from Earth's center. The average measured value near Earth's surface is 9.8 m/s².
Q2: Why do all objects fall with the same acceleration regardless of their mass?
According to Newton's law of gravitation, gravitational force is proportional to an object's mass. However, Newton's second law shows acceleration is inversely proportional to mass. These effects cancel out, making acceleration independent of mass. Therefore, all objects near Earth's surface experience the same gravitational acceleration of 9.8 m/s².
Q3: How does Earth's rotation affect the acceleration due to gravity?
The acceleration due to gravity varies from the equator to the poles because of Earth's rotation about its axis. This rotational effect causes measurable differences in g at different latitudes. However, for most practical purposes near Earth's surface, such as on Mount Everest, these variations are negligible and g can be treated as constant.
Q4: How can Earth's mass be calculated from the acceleration due to gravity?
Since Earth's mass and average radius are related to the gravitational constant and acceleration due to gravity, one can be estimated if the other is known. By substituting measured values of g, the gravitational constant, and Earth's radius into the gravitational equation, Earth's mass is calculated to be approximately 5.97 × 10²⁴ kilograms.
Q5: Does the acceleration due to gravity change significantly at high altitudes?
Near Earth's surface, g remains approximately constant at 9.8 m/s². However, at distances hundreds of kilometers above Earth's surface, the value of g becomes considerably different. This occurs because g depends on the square of the distance from Earth's center, so greater altitudes produce measurable reductions in gravitational acceleration.
Q6: What is the relationship between weight and acceleration due to gravity?
An object's weight is the gravitational force acting on it, calculated as mass times acceleration due to gravity (mg). According to Newton's second law, this force equals mass multiplied by acceleration. Since g is independent of an object's mass, weight is directly proportional to mass, with g serving as the proportionality constant.
Q7: Why is Earth considered an inertial frame of reference for studying gravity?
Although every object applies an equal and opposite gravitational pull on Earth according to Newton's third law, Earth's acceleration is negligible because its mass is vastly larger than ordinary objects near it. This makes Earth an appropriate inertial frame of reference for studying the dynamics of objects placed on or near its surface.