14.6
Aceleración debido a la gravedad en la Tierra
Según la ley de gravitación de Newton, la fuerza gravitacional sobre un cuerpo es proporcional a su masa. De acuerdo con la segunda ley del movimiento…
Se considera que un objeto está en caída libre cuando la única fuerza que actúa sobre él es la fuerza gravitacional de la Tierra. La aceleración de un objeto en caída libre de este tipo se denomina aceleración debida a la gravedad, denotada por g.
Según la segunda ley del movimiento de Newton, la magnitud de la fuerza que actúa sobre el objeto es igual a su masa por su aceleración. También se conoce como el peso del objeto.
Igualando mg con la ecuación de la fuerza gravitatoria, la aceleración debida a la gravedad del objeto se puede expresar como el producto de la constante gravitacional y la masa de la Tierra, dividida por el cuadrado de su distancia al centro de la Tierra.
El valor medio medido de g cerca de la superficie de la Tierra es de 9,8 m/s2. Dado que g es independiente de la masa del objeto, todas las masas cercanas a la superficie de la Tierra caen libremente con la misma aceleración.
Por lo tanto, sustituyendo los valores de aceleración debida a la gravedad, la constante gravitacional y la distancia como el radio de la Tierra, se estima que la masa de la Tierra es de 5,97 × 1024 kilogramos.
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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.