14.6
Przyspieszenie spowodowane grawitacją na Ziemi
Zgodnie z prawem grawitacji Newtona siła grawitacji działająca na ciało jest proporcjonalna do jego masy. Zgodnie z drugą zasadą dynamiki Newtona przy…
Uważa się, że obiekt spada swobodnie, gdy jedyną siłą działającą na niego jest siła grawitacji Ziemi. Przyspieszenie takiego swobodnie spadającego obiektu nazywa się przyspieszeniem grawitacyjnym, oznaczonym przez g.
Zgodnie z drugą zasadą dynamiki Newtona wielkość siły działającej na obiekt jest równa jego masie pomnożonej przez przyspieszenie. Jest ona również znana jako waga przedmiotu.
Zrównując mg z równaniem siły grawitacji, przyspieszenie grawitacyjne obiektu można wyrazić jako iloczyn stałej grawitacyjnej i masy Ziemi, podzielony przez kwadrat jej odległości od środka Ziemi.
Średnia zmierzona wartość g w pobliżu powierzchni Ziemi wynosi 9,8 m/s2. Ponieważ g jest niezależne od masy obiektu, wszystkie masy w pobliżu powierzchni Ziemi spadają swobodnie z tym samym przyspieszeniem.
Dlatego też, podstawiając wartości przyspieszenia ziemskiego, stałej grawitacyjnej i odległości jako promień Ziemi, masę Ziemi szacuje się na 5,97 × 1024 kilogramów.
View the full transcript and gain access to JoVE Core videos
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.