14.6
뉴턴의 중력 법칙에 따르면 물체에 작용하는 중력은 물체의 질량에 비례합니다. 뉴턴의 운동 제2법칙에 따르면 외부 힘에 의해 발생하는 가속도는 힘에 반비례합니다. 따라서 외부 중력을 받는 물체의 가속도는 물체의 질량과 무관합니다.
지구의 중력으로 인해 지구에 가까운 물체…
물체는 그 물체에 작용하는 유일한 힘이 지구의 중력일 때 자유 낙하하는 것으로 간주됩니다. 이러한 자유 낙하 물체의 가속도를 중력 가속도라고 하며 g로 표시됩니다.
뉴턴의 운동 제2법칙에 따르면 물체에 작용하는 힘의 크기는 물체의 질량에 가속도를 곱한 값과 같습니다. 물체의 무게라고도 합니다.
mg을 중력 방정식과 동일시하면 물체의 중력으로 인한 가속도는 중력 상수와 지구 질량의 곱을 지구 중심으로부터의 거리의 제곱으로 나눈 값으로 표현할 수 있습니다.
지구 표면에 가까운 g의 평균 측정 값은 9.8m/s2입니다. g는 물체의 질량과 무관하기 때문에 지구 표면 근처의 모든 질량은 동일한 가속도로 자유 낙하합니다.
따라서 중력으로 인한 가속도, 중력 상수, 거리를 지구의 반지름으로 대체하면 지구의 질량은 5.97 × 1024kg으로 추정됩니다.
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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.